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We consider the free energy of a mean-field quantum spin glass described by a p -spin interaction and a transversal magnetic field. Recent rigorous results for the case p = ∞ , i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the p -spin model converges in a joint thermodynamic and p → ∞ limit to the free energy of the QREM. [ABSTRACT FROM AUTHOR] more...

In this paper, we study the two-dimensional (2D) ultracold Fermi gas with weak impurity in the framework of mean-field theory where the impurity is introduced through Gaussian fluctuations. We have investigated the role of the impurity by studying the experimentally accessible quantities such as condensate fraction and equation of state of the ultracold systems. Our analysis reveals that at the crossover, the disorder enhances superfluidity, which we attribute to the unique nature of the unitary region and to the dimensional effect. [ABSTRACT FROM AUTHOR] more...

In this paper, we present a new mathematical rigorous technique for computing the average free energy of a disordered system with quenched randomness, using the replicas. The basic tool of this technique is a distributional zeta-function, a complex function whose derivative at the origin yields the average free energy of the system as the sum of two contributions: the first one is a series in which all the integer moments of the partition function of the model contribute; the second one, which cannot be written as a series of the integer moments, can be made as small as desired. This result supports the use of integer moments of the partition function, computed via replicas, for expressing the average free energy of the system. One advantage of the proposed formalism is that it does not require the understanding of the properties of the permutation group when the number of replicas goes to zero. Moreover, the symmetry is broken using the saddle-point equations of the model. As an application for the distributional zeta-function technique, we obtain the average free energy of the disordered model defined in a -dimensional Euclidean space. [ABSTRACT FROM AUTHOR] more...

We study the dynamics of interacting lattice fermions with random hopping amplitudes and random static potentials, in presence of time-dependent electromagnetic fields. The interparticle interaction is short-range and translation invariant. Electromagnetic fields are compactly supported in time and space. In the limit of infinite space supports (macroscopic limit) of electromagnetic fields, we derive Ohm and Joule's laws in the AC-regime. An important outcome is the extension to interacting fermions of the notion of macroscopic AC-conductivity measures, known so far only for free fermions with disorder. Such excitation measures result from the second law of thermodynamics and turn out to be Lévy measures. As compared to the Drude (Lorentz-Sommerfeld) model, widely used in Physics, the quantum many-body problem studied here predicts a much smaller AC-conductivity at large frequencies. This indicates (in accordance with experimental results) that the relaxation time of the Drude model, seen as an effective parameter for the conductivity, should be highly frequency-dependent. We conclude by proposing an alternative effective description - using Lévy processes in Fourier space - of the phenomenon of electrical conductivity. [ABSTRACT FROM AUTHOR] more...

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes. [ABSTRACT FROM AUTHOR] more...

We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic scale. The present paper belongs to a succession of studies on Ohm and Joule's laws from a thermodynamic viewpoint starting with [1-3]. We show, in particular, the existence and finiteness of the conductivity measure µS for macroscopic scales. Then we prove that, similar to the conductivity measure associated to Drude's model, µS converges in the weak*-topology to the trivial measure in the case of perfect insulators (strong disorder, complete localization), whereas in the limit of perfect conductors (absence of disorder) it converges to an atomic measure concentrated at frequency ν = 0. However, the AC-conductivity µS|R\{0} does not vanish in general: We show that µS(R\{0}) > 0, at least for large temperatures and a certain regime of small disorder. [ABSTRACT FROM AUTHOR] more...

Quantum mechanics manifests in experimental observations in several ways. Hauge et al. (1987) and Leavens et al. (1989) had pointed out that interference effects dominate a physical quantity called injectance. We show that, very paradoxically, the interference related term vanish in a quantum regime making semi-classical formula for injectance exact in this regime. This can have useful implications to experimentalists as semi-classical formulas are much more simple. There are other puzzling facts in this regime like an ensemble of particles that can be transmitted without any time delay or negative time delays. [ABSTRACT FROM AUTHOR] more...

In the last few years, the statistical mechanics of spin glasses has become one of the major frameworks for analyzing the macroscopical equilibrium properties of complex systems starting from the microscopical dynamics of their components. Recently, many advances in its rigorous formulation without the replica trick have been achieved, highlighting the importance of this field of research in our understanding of complex systems. In this framework we analyze the critical behavior of a Poissonian diluted network with random competitive interactions among gauge-invariant dichotomic variables pasted on the nodes (i.e., a suitable version of the Viana-Bray diluted spin glass). The model is described by an infinite series of order parameters (the multioverlaps) and has two degrees of freedom: the temperature (which can be thought of as the noise level) and the connectivity (the averaged number of links per node in the underlying network). In this paper, we show that there are not several transition lines, one for every order parameter, as a naive approach would suggest but just one corresponding to ergodicity breaking. We explain this scenario within a novel and simple mathematical technique: we show the existence of a driving mechanism such that, as the first order parameter (the two-replica overlap) becomes different from zero due to a real second order phase transition, it enforces all the other multioverlaps toward positive values thanks to the strong correlations which develop among themselves and the two-replica overlap at the critical line. These correlations are ultimately related - within our framework - to the breaking of the gauge invariance of the Boltzmann state at the boundary of the ergodic region. A discussion on the structure of the free energy, fundamental macroscopical observable by which the whole thermodynamic can be achieved, is also presented. [ABSTRACT FROM AUTHOR] more...

We present here an optimized and parallelized version of the augmented space recursion code for the calculation of the electronic and magnetic properties of bulk disordered alloys, surfaces and interfaces, either flat, corrugated or rough, and random networks. Applications have been made to bulk disordered alloys to benchmark our code. [ABSTRACT FROM AUTHOR] more...

A concise and somewhat personal review of the problem of superfluidity and quantum criticality in regular and disordered interacting Bose systems is given, concentrating on general features and important symmetries that are exhibited in different parts of the phase diagram, and that govern the different possible types of critical behavior. A number of exact results for various insulating phase boundaries, which may be used to constrain the results of numerical simulations, can be derived using large rare region type arguments. The nature of the insulator-superfluid transition is explored through general scaling arguments, exact model calculations in one dimension, numerical results in two dimensions, and approximate renormalization group results in higher dimensions. Experiments on 4He adsorbed in porous Vycor glass, on thin film superconductors, and magnetically trapped atomic vapors in a periodic optical potential are used to illustrate many of the concepts. [ABSTRACT FROM AUTHOR] more...

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined on random directed graphs with constant out-degrees and evolve according to cellular automaton rules. For some families of rules, a few typical a priori unexpected results are presented. [ABSTRACT FROM AUTHOR] more...

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field (E) and a field of rotational nature (B) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of E field and intensities of both E and B fields in two-dimensions. The system shows interesting and unusual critical behavior at the percolation threshold. Not only the DSP model is found to belong in a new universality class compared to that of other percolation models but also the universality class remains invariant under the variation of E field direction. Varying the intensities of the E and B fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields E and B. [ABSTRACT FROM AUTHOR] more...

A model of the opinion dynamics underlying the political decision is proposed. The analysis is restricted to a bipolar scheme with a possible third political area. The interaction among voters is local but the final decision strongly depends on global effects such as the rating of the governments. As in the realistic case, the individual decision making process is determined by the most relevant personal interests and problems. The phenomenological analysis of the national vote in Italy and Germany has been carried out and a prediction of the next Italian vote as a function of the government rating is presented. [ABSTRACT FROM AUTHOR] more...

To explain experimentally observed quasiparticle relaxation rates in the cuprate superconductors, Sachdev and collaborators recently proposed that the d-wave system may be close to a quantum critical point towards a superconducting state with an additional order parameter component of is- or id-wave symmetry. In the proximity of the transition, dynamical order parameter fluctuations modify the system properties. Here, we explore the influence of disorder on this interacting fluctuation regime. Our main finding is that unlike in the clean system, significant qualitative differences between is and id exist: In the is-case, due to the disorder-enhanced low-energy density of states, a secondary superconducting transition (with a strongly disorder-dependent Tc) takes place. In contrast, in the id-case essential features of the clean scenario are left intact by the disorder. [ABSTRACT FROM AUTHOR] more...

We review a recent development in theoretical understanding of the quenched averaged correlation functions of disordered systems and the logarithmic conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field theory is the generalization of the conformal field theory when the dilatation operator is not diagonal and has the Jordan form. It is discussed that at the random fixed point the disordered systems such as random-bond Ising model, Polymer chain, etc. are described by LCFT and their correlation functions have logarithmic singularities. As an example we discuss in detail the application of LCFT to the problem of random-bond Ising model in 2≤d≤4. [ABSTRACT FROM AUTHOR] more...