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Abstract We investigate the phase diagram of a spin-1 ferromagnetic XY model in the presence of a longitudinal easy-axis crystal field assuming bilinear (J) and biquadratic (I) exchange interactions between nearest neighbors spins and using the two-time Green Functions framework at the level of the Devlin strategy. Employing both analytical estimates and numerical calculations, we find that the structure of the crystal-field-induced phase boundary changes sensibly as the ratio $$\alpha = I/J$$ α = I / J increases. In particular, when $$\alpha $$ α overcomes a characteristic value $$\alpha ^*$$ α ∗ , two quantum critical points appear which are connected by a dome-shaped critical line. Due to the paradigmatic nature of the anisotropic spin model here considered, we believe that our findings may provide useful insights into the physical origin of recent experimental results found for some innovative materials which exhibit two quantum critical points and dome-shaped phase diagrams induced by non-thermal control parameters driving a non-conventional quantum criticality. Graphic abstract

We used the two-time Green function framework to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of ( d > 2 )-dimensional spin-1planar ferromagnets, which exhibit a magnetic field induced quantum phase transition. We tackled the problem using two different kind of approximations: the Anderson-Callen decoupling scheme and the Devlin approach. In the latter scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point, for certain values of the single-ion anisotropy parameter. We compare the results obtained within the two approximation schemes. In particular, we recover the same qualitative behavior. We show the phase diagram, close to the field-induced quantum critical point and the behavior of the susceptibility for different values of the single-ion anisotropy parameter, enhancing the differences between the two different scenarios (i.e. with and without reentrant behavior).

The Devlin two-time Green function framework is used to investigate the role played by the easy-axis single-ion anisotropy on the phase diagram of ( d > 2 ) -dimensional spin-1 planar ferromagnets which exhibit a magnetic-field-induced quantum phase transition (QPT). In this scheme, the exchange anisotropy terms in the equations of motion are treated at the Tyablikov decoupling level while the crystal field anisotropy contribution is handled exactly. The emerging key result is a reentrant structure of the phase diagram close to the quantum critical point for a well defined window of values of the single-ion anisotropy parameter. This experimentally interesting feature was recently recovered by employing the Anderson-Callen decoupling (ACD) which is considered to provide meaningful results only for small values of the single-ion anisotropy parameter. In this context, our findings suggest that the simplest ACD treatment offers the possibility to have, at least qualitatively, a correct physical scenario of quantum criticality close to a field-induced QPT avoiding the limiting mathematical difficulties involved in the Devlin scheme.

In this work we study the quantum phase transition, the phase diagram and the quantum criticality induced by the easy-plane single-ion anisotropy in a d-dimensional quantum spin-1 XY model in absence of an external longitudinal magnetic field. We employ the two-time Green function method by avoiding the Anderson–Callen decoupling of spin operators at the same sites which is of doubtful accuracy. Following the original Devlin procedure we treat exactly the higher order single-site anisotropy Green functions and use Tyablikov-like decouplings for the exchange higher order ones. The related self-consistent equations appear suitable for an analysis of the thermodynamic properties at and around second order phase transition points. Remarkably, the equivalence between the microscopic spin model and the continuous O ( 2 ) - vector model with transverse-Ising model (TIM)-like dynamics, characterized by a dynamic critical exponent z=1, emerges at low temperatures close to the quantum critical point with the single-ion anisotropy parameter D as the non-thermal control parameter. The zero-temperature critic anisotropy parameter Dc is obtained for dimensionalities d > 1 as a function of the microscopic exchange coupling parameter and the related numerical data for different lattices are found to be in reasonable agreement with those obtained by means of alternative analytical and numerical methods. For d > 2 , and in particular for d=3, we determine the finite-temperature critical line ending in the quantum critical point and the related TIM-like shift exponent, consistently with recent renormalization group predictions. The main crossover lines between different asymptotic regimes around the quantum critical point are also estimated providing a global phase diagram and a quantum criticality very similar to the conventional ones.

The two-time Green function method is employed to explore the effect of the biquadratic exchange interaction on the phase diagram of a $d$-dimensional spin-1 transverse XY model with single-ion anisotropy close to the magnetic-field-induced quantum critical point. We work at level of the Anderson-Callen-decoupling-like framework for both easy-plane and easy-axis single-ion anisotropy. The structure of the phase diagram is analyzed with analytical estimates and numerical calculations by adopting Tyablikov-like decouplings for the exchange higher order Green functions in the equation of motion. For dominant bilinear short-range exchange interaction the structure of the phase diagram close to the quantum critical point remains qualitatively the same of that in absence of biquadratic interaction including reentrant critical lines. When the biquadratic exchange becomes increasingly dominant its role appears more effective and tends to reduce or destroy the reentrant character of the critical lines., 22 pages, 5 figures

The low-temperature critical properties of the three-dimensional spin-1 XY model with an easy-plane single-ion anisotropy in zero magnetic field are explored on the ground of a path-integral representation and of the momentum-shell renormalization group where the single-ion anisotropy parameter drives a quantum phase transition. We address this problem first deriving systematically a suitable quantum Ginzburg–Landau–Wilson functional whose structure suggests, in a transparent way, that the microscopic spin model is equivalent to a continuous O ( 2 ) - vector one with transverse-Ising-like intrinsic dynamics (dynamic critical exponent z=1). Then, the relevant physics close to the quantum critical point is extracted from the appropriate one-loop Wilsonian flow equations. In particular we calculate the zero-temperature critical value of the anisotropy parameter for different cubic lattices. We compare our findings with those obtained in the literature by means of alternative methods and of experiments on praseodymium. The critical line ending in the quantum critical point is also calculated and the related shift exponent is determined. Finally, by solving in different asymptotic regimes the self-consistent equation for transverse susceptibility, a finite-temperature quantum critical scenario emerges which is quite similar to the conventional ones.

The classical to quantum crossover, which occurs in d-dimensional transverse field Ising model-like systems decreasing the temperature to zero in the influence domain of the quantum critical point (QCP), is described by employing an effective Wilsonian renormalization group approach in 4 - e dimensions. The basic ingredient of the treatment is the static action arising from a preliminary one-loop averaging over non-zero frequency modes, which enter the original quantum one. The crossover scaling functions for susceptibility and related thermodynamic quantities are obtained to first order in e as explicit functions of the temperature and the applied magnetic field. In our static framework, which can be easily extended to other quantum systems exhibiting a critical line which terminates in a QCP, the suitable procedure for observing this type of crossover through genuine thermodynamic measurements is clarified consistently with available experiments. Remarkably, our basic idea and results may be usefully employed to explore also the dimensional crossover which takes place in classical Ising-like systems with slab or film geometry and, possibly, in other finite-size classical systems.

We investigate the role played by symmetry conserving quenched disorder on quantum criticality of a variety of d-dimensional systems with a continuous symmetry order parameter.We employ a non standard procedure which combines a preliminary reduction to an effective classical problem and a successive renormalization group treatment. We find a quantum critical point scenario exhibiting unusual features, which remind us of some predictions of the quantum Griffiths phase model

We revisit quantum criticality of d -dimensional n -vector transverse Ising-like models by means of a conventional one-loop renormalization group (RG) approach with temperature scaling. Focusing on dimensionalities d ≤ 3 , a careful analysis of the quantum regime allows us to explore the low-temperature phase diagram and to derive new features which occur close to but below the quantum critical point within the disordered phase. In particular, for d 3 a crossover of the shift exponent from the value ψ = d − 1 (as for d > 3 ) to ψ = 2 is found by decreasing the temperature to zero. Besides we provide information about the low-temperature physics within the thermally disordered region usually ignored in the literature. A similar scenario takes place for d = 3 , but now logarithmic corrections to the mean-field power-law behavior are involved.

Within the Wilson Renormalization Group (WRG) approach as applied to d -dimensional quantum systems using appropriate functional representations, we develop a general method for describing the critical behaviour driven by the temperature T when the quantum fluctuations are into play. It consists in solving the quantum RG equations near a zero-temperature fixed point (FP) introducing T -dependent scaling fields which are determined by ordinary first-order differential equations with appropriate boundary conditions. This allows us to explore, in a unified and relatively simple way, the low-temperature properties near a ( T = 0)-quantum instability of a great variety of quantum systems (interacting Bose gas, quantum ferroelectrics, itinerant fermion materials, spin models in a tranverse field, granular superconductors, etc.). The crossover from the low-but finite-temperature critical behaviour to the quantum criticality is also described in a natural way in terms of appropriate effective exponents. The predictions appear to be quite quantum systems by means of different approaches. For the interacting Bose gas and other quantum systems lying in the same universality class (bosonic systems), our results give us the opportunity to rexamine some uncorrect calculations for d ≤2 recently appeared in the literature.

The effects of single-ion anisotropy on quantum criticality in a d-dimensional spin-S planar ferromagnet is explored by means of the two-time Green’s function method. We work at the Tyablikov decoupling level for exchange interactions and the Anderson-Callen decoupling level for single-ion anisotropy. In our analysis a longitudinal external magnetic field is used as the non-thermal control parameter and the phase diagram and the quantum critical properties are established for suitable values of the single-ion anisotropy parameter D. We find that the single-ion anisotropy has sensible effects on the structure of the phase diagram close to the quantum critical point. However, for values of the uniaxial crystal-field parameter below a positive threshold, the conventional magnetic-field-induced quantum critical scenario remains unchanged.

We have revisited quantum criticality of d- dimensional n-vector transverse Ising-like models by means of a one-loop renormalization group approach with temperature scaling. A careful analysis of the quantum regime for d ≤ 3 allows us to explore the low-temperature phase diagram and to derive new features which occur close to the quantum critical point within the disordered phase. In particular for d ≤ 3 a crossover of the shift exponent from the value ψ = d-1 ( as for d ≥ 3 ) to ψ = 2 is found decreasing the temperature to zero.

A d -dimensional model of multicomponent interacting bosons with spin S and a magnetic moment in the presence of a magnetic field H is studied by means of a large- n limit treatment and a renormalization group approach, in the spirit of critical phenomena theory. Magnetic phase transitions and a ferromagnetic state with a zero-field divergent susceptibility and an exotic criticality are shown to occur, as in the noninteracting model, strictly related to the onset of the Bose-Einstein condensation. The bosonic and magnetic properties of the system are explored by approaching a critical line which marks, for H ≠ 0, the occurrence of Bose-Einstein transitions together with magnetic ones whose order, greater than two, depends on the ratio d / θ , where 0 θ ≤ 2 is connected to the range of interactions (in the n -vector classical counterpart).

Criticality of n-vector quantum systems is studied, via a renormalization group treatment, assuming a pair interaction which decays as a power law involving a characteristics parameter θ. Within a “single”-expansion parameter scheme for finite values of θ, a novel fixed point appears for nonbosonic systems both in the classical and quantum regimes and for bosonic ones only in the classical regime. Under certain conditions, it governs a new criticality which exhibits superuniversality with respect to the symmetry of the order parameter and absence of dimensional crossover. An interesting aspect of the formalism is that it allows us to investigate the critical properties of a wide class of systems at realistic dimensionalities suggesting new experimental possibilities. For infinitesimal values of θ, a “double”-expansion parameter scheme yields two new accessible fixed points which, surprisingly, control the same criticality with restored dimensional crossover for nonbosonic systems. For bosonic systems in the quantum regime, the long-range tail in the interaction induces a runaway which signals the absence of any sharp second-order transition in contrast with the usual short-range scenario.

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3, Comment: 9 pages, 2 figures; to be published on EPJB

The Wilson renormalization group is used to investigate the low-temperature critical properties of a spin- 1 2 Heisenberg ferromagnet with easy-plane anisotropy in a transverse field. The phase diagram and the main critical exponents close to the quantum critical point are obtained for dimensionalities d>2. Crossover phenomena are found to occur decreasing the temperature and the related effective exponents are determined.

The low-temperature properties and crossover phenomena of $d$-dimensional transverse Ising-like systems within the influence domain of the quantum critical point are investigated solving the appropriate one-loop renormalization group equations. The phase diagram is obtained near and at $d=3$ and several sets of critical exponents are determined which describe different responses of a system to quantum fluctuations according to the way of approaching the quantum critical point. The results are in remarkable agreement with experiments for a wide variety of compounds exhibiting a quantum phase transition, as the ferroelectric oxides and other displacive systems., Comment: 36 pages, 2 figures, accepted in Physica A

The critical properties of the d -dimensional transverse Ising model in the influence domain of its quantum critical point are studied solving the one-loop renormalization group equations around and at d =3. Different critical regimes occur involving crossover behaviours which can be described in terms of effective exponents, consistently with the conventional crossover theory.

We investigate the low-temperature critical properties of a classical Ising model in a transverse field. This is performed by applying the conventional Wilson renormalization group to the related Ginzburg-Landau functional emerging from a Hubbard-Stratonovich transformation. Results in 4–e dimensions provide a low temperature critical scenario very similar to that found for the quantum counterpart. Remarkably, we find that the discrimination between the two cases essentially lies on the different values of the shift exponent which characterizes the behavior of the phase boundary close to the zero-temperature critical point. This feature suggests that, decreasing the temperature, the observation of different renormalized critical exponents may signal activation of genuine quantum critical fluctuations.

The two-time Green's function method is used to study the critical properties and crossover phenomena near the field-induced quantum critical point (QCP) of a $d$-dimensional spin-$S$ planar Heisenberg ferromagnet with long-range interactions decaying as ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ (with $\ensuremath{\alpha}gd$) with the distance $r$ between spins. We adopt the Callen scheme for spin $S$ and the Tyablikov decoupling procedure which is expected to provide suitable results at low temperatures. Different quantum critical regimes are found in the $(\ensuremath{\alpha},d)$ plane and the global structure of the phase diagram is determined showing the typical V-shaped region close to the QCP. Depending on the values of $\ensuremath{\alpha}$, we find that also for dimensionalities $d\ensuremath{\leqslant}2$ a finite-temperature critical line, ending in the QCP, exists with asymptotic behaviors and crossovers which can be employed as a useful guide for experimental studies. Moreover, these crossovers are shown to be suitably described in terms of $(\ensuremath{\alpha},d)$-dependent scaling functions and effective critical exponents.

A reduction procedure, suggested for classical systems some years ago, is extended to systems with quantum-phase transitions with the aim to generate exactly solvable models capturing fluctuation effects beyond the mean field approximation. For the reduced isotropic m -vector quantum models, an exact nonperturbative renormalization group formulation is presented and the relation to the classical counterpart is established. We show that, with a simple change of the coupling functional, it is possible to reproduce formally the flow differential equations already obtained in the large- m limit many years ago. The substantial difference is that the reduction procedure used here does not impose any restriction on the dimension m of the order parameter field.

We analyze the effects induced by single-ion anisotropy on quantum criticality in a d-dimensional spin-3/2 planar ferromagnet. To tackle this problem we employ the two-time Green's function method, using the Tyablikov decoupling for exchange interactions and the Anderson-Callen decoupling for single-ion anisotropy. In our analysis the role of non-thermal control parameter which drives the quantum phase transition is played by a longitudinal external magnetic field. We find that the single-ion anisotropy has substantial effects on the structure of the phase diagram close to the quantum critical point.

The two-time Green function method is employed to explore the phase diagram and the magnetic-field-induced quantum criticality of a three-dimensional spin-one planar ferromagnet with easy-axis single-ion anisotropy. We adopt the Tyablikov and Anderson-Callen decouplings for higher order exchange and single-ion anisotropy Green functions, respectively. The central finding is that, within a characteristic range of the anisotropy parameter values, reentrant phenomena occur in the phase diagram close to the quantum critical point producing a sensible change of the conventional quantum critical scenario.

The low temperature critical properties and crossovers of a spin 1/2 planar ferromagnet in a longitudinal magnetic field are explored in 4-e dimensions in terms of an anisotropic action, suitable to describe the spin model in the low temperature regime. This is performed adopting a procedure whivh combines a preliminary averaging over dynamic degrees of freedom and a next static Wilson renormalization group transformation.

The one-loop renormalization group equations are derived and analysed for a wide class of quantum statistical models describing the critical behaviour of systems with short-range correlated random impurities. The classical and quantum critical properties are considered to first order in a double e-expansion. It is proven that the quantum critical behaviour of disordered systems with short-range random correlation is equivalent to the classical critical behaviour of certain systems with extended random impurities. The reliability of the double e-expansion method and the interpretation of the results are discussed.

A nonconventional renormalization-group (RG) treatment close to and below four dimensions is used to explore, in a unified and systematic way, the low-temperature properties of a wide class of systems in the influence domain of their quantum critical point. The approach consists in a preliminary averaging over quantum degrees of freedom and a successive employment of the Wilsonian RG transformation to treat the resulting effective classical Ginzburg-Landau free energy functional. This allows us to perform a detailed study of criticality of the quantum systems under study. The emergent physics agrees, in many aspects, with the known quantum critical scenario. However, a richer structure of the phase diagram appears with additional crossovers which are not captured by the traditional RG studies. In addition, in spite of the intrinsically static nature of our theory, predictions about the dynamical critical exponent, which parametrizes the link between statics and dynamics close to a continuous phase transition, are consistently derived from our static results.

The effect of quenched impurities on the quantum critical behaviour of dilute Bose systems is investigated with the help of renormalization group and double ϵ-expansion methods. It is shown that the presence of quenched impurities leads to an instability of the zero temperature quantum critical behaviour.

A non-conventional point of view is used to explore the still unclear role played by the competition between quenched disorder and quantum fluctuations in systems which exhibit a quantum phase transition in the clean limit. The approach consists in averaging over quantum degrees of freedom and next in applying the renormalization group transformation to the resulting effective classical random action. It emerges that, below four dimensions, the quantum criticality appears to be controlled by the classical random fixed point. (c) 2006 Elsevier B.V. All rights reserved.

The field-induced quantum criticality of compounds with ferromagnetically coupled structural spin units (as dimers and ladders) is explored by applying Wilson's renormalization group framework to an appropriate effective action. We determine the low-temperature phase boundary and the behavior of relevant quantities decreasing the temperature with the applied magnetic field fixed at its quantum critical point value. In this context, a plausible interpretation of some recent experimental results is also suggested., Comment: to be published in Physics Letters A

A one-loop renormalization group treatment is used to investigate the quantum phase transition and the low-temperature critical properties of a planar Heisenberg ferromagnet in a transverse field. The phase diagram, the free energy density and the relevant critical exponents in the influence domain of the quantum critical point are obtained for dimensionalities d ⩾ 2 in the temperature regime where the quantum fluctuations dominate. The ( d = 2 ) -criticality is also studied decreasing the temperature with the magnetic field fixed at its critical value. The method of calculation and the peculiarity of the model allow us to work systematically within the region around the critical line where the quantum degrees of freedom govern the low-temperature critical behavior of the model.

We suggest a general procedure to analyze quantum criticality for a wide variety of quantum systems of topical interest, close and below four dimensions. The idea is to apply the Wilsonian renormalization group philosopy to an effective classical functional derived from the general quantum action by averaging over degrees of freedom with non zero Matsubara frequencies. This allows to describe in an unified way all crossovers expected close to a quantum critical point

A simple infinite-range model of axial quadrupolar glass is investigated within the cavity-fields approach inside a pure state and a cluster of pure states. Working at a level of a pure state, the nonlinear susceptibility is de- rived. When a cluster of pure states is considered, all the known results of the one-step replica-symmetry breaking approach are easily reproduced. Besides, the nonlinear susceptibility and the stability conditions are obtained and re- lated numerical results are presented. In this way the stability range of the replica-symmetry breaking solution, quite difficult to be derived within the replica method, is established on the purely physical ground. An interesting feature is that, at any considered stage, the nonlinear susceptibility diverges at a given temperature 71 where the quadrupolarization and the quadrupo- lar glass order parameters are nonzero and finite. Tlis may be interpreted as a signal of a glassy phase transition not in the Landau sense.

A simple infinite-range model of axial quadrupolar glass is investigated within the cavity-fields approach inside a pure state and a cluster of pure states. Working at the level of a pure state, the Thouless-Anderson-Palmer (TAP)\char21{}like equations and the nonlinear susceptibility are derived and the thermodynamic stability conditions are obtained in a transparent physical way. At this first stage, the cavity-fields results agree with those previously achieved within the replica-symmetric scheme. At the second stage of the cavity method, where a cluster of pure states is considered, all the known results of the one-step replica-symmetry breaking approach are easily reproduced. Besides the TAP-like equations for the quadrupolar ancestor, the nonlinear susceptibility and the stability conditions are obtained and related numerical results are presented. In this way the stability range of the replica-symmetry breaking solution, quite difficult to be derived within the replica method, is established on the purely physical ground. An interesting feature is that, at any considered stage, the nonlinear susceptibility diverges at a given temperature ${\mathit{T}}_{\mathit{c}}$ where the quadrupolarization and the quadrupolar glass order parameters are nonzero and finite. This may be interpreted as a signal of a glassy phase transition not in the Landau sense. \textcopyright{} 1996 The American Physical Society.

The Ising infinite-range spin-glass model with p-spin interactions in the presence of a transverse field is studied for large but finite p using the Matsubara time representation and Parisi's scheme of replica-symmetry breaking. In the spin-glass phase, the corrections to the limit appear much more essential than in the classical counterpart. It is shown that the quantum fluctuations have the effect of destroying the spin-glass order and a lower temperature is required to stabilize the spin-glass phase. The spin autocorrelation function in the spin-glass phase is explicitly calculated as a function of p and the Matsubara time. The result is just complementary and consistent with that previously obtained for the paramagnetic state without using the replica method.

A nonconventional renormalization group procedure, which involves fixed points and eigenvectors depending on temperature T , is proposed to describe classical-quantum crossover phenomena for quantum systems near criticality. In this new picture, T -dependent critical exponents occur, where T assumes the role of a natural crossover parameter.

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

We study the effects of correlated symmetry-breaking-like random fields on critical properties of a d-dimensional sine-Gordon model. A Wilsonian renormalization group analysis shows an unusual scenario in the absence of stable fixed points. The physical nature of the related runaway in the parameter space is investigated by means of a complementary variational treatment. Self-consistent predictions for d>1 suggest that the disorder of the type considered here inhibits any phase transition with diverging correlation length and that the system lives in a “glassy-phase” at all temperatures.

Double expansion renormalization group treatments are still employed in literature to describe the effects of symmetry-conserving quenched disorder on quantum phase transitions as an alternative to more or less phenomenological models. If one assumes = 4 – d and the dimensionality τ of the imaginary-time space involved in a generalized quantum action as simultaneously small parameters, a stable random fixed point is found which governs a new disorder-induced quantum criticality usually considered meaningful also after extrapolation to the physical time-like dimension τ = 1. In contrast, by considering τ = 1 at the beginning, a runaway takes place in the parameter space for dimensionalities d < 4. To give some insight into these contrasting results, we employ here a simple self-consistent approach for case of short-range correlated quenched disorder which allows us to analyze analytically what happens by continuous variation of the fictitious time-like dimension τ We find that a τ*(n) < 1 exists, depending on the symmetry index n, above which the disorder inhibits the occurrence of a conventional quantum phase transition. This suggests that the usual procedure to extrapolate the small τ-predictions to the value of interest τ = 1 may have no real physical meaning.

The low temperature critical properties and crossovers of a spin 1/2 planar ferromagnet in a longitudinal magnetic field are explored in 4-e dimensions in terms of an anisotropic action, suitable to describe the spin model in the low temperature regime. T

The infinite-range quantum XY spin-glass model in the presence of a transverse field is considered and its phase diagram is determined using the two-spin cluster expansion method. It is shown that a spin-glass phase transition is possible for non-zero transverse field up to a zero-temperature value which equals twice the largest eigenvalue of the random bond interaction matrix.

The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method. The finite-size crossover in impure films has been considered on the basis of the fundamental relationship between the effective spatial dimensionality and the characteristic lengths of the system. The difference between the critical properties of infinite systems and films is demonstrated and investigated. A new critical exponent, describing the scaling properties of the thickness of films with extended impurities has been deduced and calculated. A special attention is paid to the critical behaviour of real impure films., 27 pages LaTex; figures are available in the journal variant

We suggest a general procedure to analyze quantum criticality for a wide variety of quantum systems of topical interest, close and below four dimensions. The idea is to apply the Wilsonian renormalization group philosophy to an effective classical functional derived from a general quantum action by averaging over degrees of freedom with non-zero Matsubara frequencies. This allows us to describe, in an unified way, all crossovers expected close to a quantum critical point.

The low-temperature critical properties and crossovers of a spin-½ planar ferromagnet in a longitudinal magnetic field are explored in terms of an anisotropic bosonic action, suitable to describe the spin model in the low-temperature regime. This is performed adopting a procedure which combines an averaging over dynamic degrees of freedom and the classical Wilson renormalization group transformation. Within this framework we get the phase boundary, ending in a quantum critical point, and general expressions for the correlation length and susceptibility as functions of the temperature and the applied magnetic field within the disordered phase. In particular, two crossovers occur decreasing the temperature with the magnetic field fixed at its quantum critical point value, which might be actually observable in complex magnetic compounds, as suggested by recent experiments.

The critical behaviour of a dilute spin-S Bose gas in a magnetic field is investigated with the help of the renormalization group method. A complete set of critical exponents is given both at constant pressure and constant density. The magnetic properties are also discussed.

The classical transverse field Ising spin- glass model with short-range interactions is investigated beyond the mean- field approximation for a real d- dimensional lattice. We use an appropriate nontrivial modification of the Bethe- Peierls method recently formulated for the Ising spin- glass. The zero- temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d. The phase diagram is also calculated numerically for different values of d. In the limit d -> infinity, known mean- field results are consistently reproduced., LaTex, 11 pages, 2 figures

The cavity-fields approach, recently developed for studying the Sherrington-Kirkpatrick model of spin glasses and its quantum version, is appropriately reformulated for the infinite-range XY spin-glass model in a transverse field. The equations for the phase diagram of the model are obtained and preliminary numerical results are also presented.