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The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable, metastable and unstable branches of the order parameters are obtained. According to the stable conditions at critical point, we find that the systems exhibit tricritical points. With crystal field and biquadratic interactions, the system has rich phase diagrams with single reentrant or double reentrant phase transitions for appropriate ranges of the both parameters. [ABSTRACT FROM AUTHOR]

The quantum entanglement and quantum phase transition of the transverse-field Ising model on a two-dimensional square lattice were investigated by applying the quantum renormalization group method. The quantum critical point (QCP) and the correlation length exponent, ν , were obtained. By taking the concurrence as a measure of entanglement, the entanglement between spin blocks near the QCP is calculated as the size of the system becomes large. The entanglement reaches a maximum close to QCP, and can exist in a small range around QCP just at the limit of thermodynamics. The nonanalytic behavior of the derivative of the entanglement with the external field shows that the system undergoes a second order quantum phase transition from a ferromagnetic phase to a paramagnetic phase. The finite-size scaling behavior of the entanglement is described, and the relationship between the entanglement exponent, θ , the correlation length exponent, ν , and the dimension of the system d is also found, i.e., θ = 1 / ( ν d ) . [ABSTRACT FROM AUTHOR]

In this paper, the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied. By means of the recurrence relation method in the high-temperature limit, we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution. It is found that when the standard deviation of random exchange coupling δJ (or the standard deviation of random external field δB) is small, the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one. However, when δJ (or δB) is large, the crossover vanishes, and the system shows a central-peak behavior or the most disordered one. We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions. Our results show that for all the cases considered, the dynamics of the above system is similar to that of the one-dimensional random XY model. [ABSTRACT FROM AUTHOR]

Abstract: Using semiclassical method, Bose–Einstein condensation (BEC) of a relativistic ideal Bose gas (RIBG) with and without antibosons in the three-dimensional (3D) harmonic potential is investigated. Analytical expressions for the BEC transition temperature, condensate fraction, specific heat and entropy of the system are obtained. Relativistic effects on the properties of the system are discussed and it is found that the relativistic effect decreases the transition temperature T c but enlarges the gap of specific heat at T c . We also study the influence of antibosons on a RIBG. Comparing with the system without antibosons, the system with antibosons has a higher transition temperature and a lower Helmholtz free energy. It implies that the system with antibosons is more stable. [Copyright &y& Elsevier]

The ferromagnetic properties of the spin-1 BEG model on finite-size Cayley tree are investigated using the exact recursion method. The spontaneous magnetization of the system is studied in detail for different values of the reduced crystal-field interaction D/J, and it is found that there is an unusual behavior (anti-Curie temperature) when D/J > 2.0. We also obtain the Curie temperature of this finite-size system. When the system size is large enough, our results will fit well with that in the thermodynamic limit. [ABSTRACT FROM AUTHOR]

Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Gaussian model built on two typical small-world networks is studied. The results show much difference from the classical case, and thus may induce some more accurate discussion on the critical properties of the spin-lattice systems combined with the small-world networks. [ABSTRACT FROM AUTHOR]

The q-deformed Bose–Einstein distribution is used to study the Bose–Einstein condensation (BEC) of a q-deformed Bose gas in random box. It is shown that the BEC transition temperature is lowered due to random boundary conditions. The effects of q-deformation on the properties of the system are also discussed. We find some properties of a q-deformed Bose gas, which are different from those of an ordinary Bose gas. Similar results are also shown for q-bosons confined in a harmonic oscillator potential well. [ABSTRACT FROM AUTHOR]

Abstract: The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the case of bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the case of Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as increase, especially when ( and are the exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak (). [Copyright &y& Elsevier]

Abstract: Using the two-spin cluster mean-field method, the spin-1 Heisenberg model with Dzyaloshinskii–Moriya (DM) interactions is studied for the simple cubic lattice. For the case of the DM vector coupling (D is the DM interaction parameter and is the unit vector of the z-axis direction), the phase diagram of this system and the thermal behavior of the magnetization are obtained, and it is found that the system exhibits the tricritical point. The critical behavior of the system may be interpreted as a result of a competition between the exchange interaction and the DM interaction. [Copyright &y& Elsevier]

Abstract: The ferromagnetic mixed spin- and spin- Blume–Capel model on the two-fold Cayley tree is investigated using the exact recursion relations. The thermal behavior of magnetizations is studied in detail for different values of the crystal-field interaction and the coordination number of the sites of the Cayley tree. The exact phase diagrams in the plane are obtained for different . The results show that there is no tricritical behavior for the cases of all the coordination numbers and different values of crystal-field interaction. However, there are some interesting phenomena in this system, due to the crystal-field interaction. [Copyright &y& Elsevier]

Abstract: With the consideration of local events and preferential attachment, the extended model proposed by Albert and Barabási is studied. Firstly, the extended model is built only by local events. It is found that without preferential attachment the networks’ connectivity distribution decays exponentially for large connectivity, and the decaying exponent varies with different probabilities of the addition of new links and rewiring. Secondly, the extended model with partial preferential attachment is studied. When preferential attachment only presents in the addition of new links or new nodes, there is scale-free regime in the phase diagram; while preferential attachment is brought into the rewiring, there coexist two regimes, i.e., the exponential regime and the scale-free regime. Thirdly, fitness is introduced to the extended model with complete preferential attachment. It is obtained that the network''s connectivity distribution is a result affected by many factors, including the fitness, the local events and preferential attachment. [Copyright &y& Elsevier]

Abstract: We study the critical properties of the model on diamond-type hierarchical lattices in the presence of an external magnetic field. It is assumed that for this type of inhomogenous fractal lattice, the Gaussian distribution constant, the four-spins interaction parameter and the external magnetic field in the model depend on the coordination number of the site on the fractal lattices. By combining the real-space renormalization-group scheme with the cumulative expansion method, we obtain the critical points and further calculate critical exponents according to the scaling theory. The results show that on diamond-type hierarchical lattices with branches of 2 bonds, the critical point of the model is just the Gaussian fixed point, and therefore critical exponents are in full agreement with those of the Gaussian model, and that on those with , the Wilson–Fisher fixed point as well as the Gaussian fixed point is obtained. The Wilson–Fisher fixed point has a decisive influence on the critical behavior of the system, and critical exponents are related to the fractal dimensionality. We found that the model on the fractal lattices and that on the translation symmetric lattices show similar behaviors in the dependence of the critical properties on the dimensionality. [Copyright &y& Elsevier]

Using the one-dimensional Vlasov-Poisson simulation method, the nonlinear cold-electron-plasma oscillations against a fixed periodic ion background are studied. It is shown that a gradual loss of the phase coherence in the excited Langmuir wave dynamics occurs in such plasmas leading to wave-breaking at arbitrary low wave amplitudes. Not only the salient features of a steepening of the electric field gradient and large electron density peaks caused by the presence of the ion cavities have been found but also the change of phase-mixing and burst time with the initial ion density perturbation and electron temperature has been studied. The evolution processes of the electron distributions in phase space, especially the electron distribution at the phase-mixing and burst time, have been studied. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the non-Hermitian spin-1/2 XY model in the presence of the alternating, imaginary and transverse magnetic fields. For the two-site spin system, we solve exactly the energy spectrum and phase diagram and also calculate the ground-state and thermal entanglements by using the concept of the concurrence. It is found that the two-site concurrence in the eigenstate which only depends on the imaginary magnetic field η is always equal to one in the region of P T symmetry, while it decreases with η in the P T -symmetric broken region; especially, the first derivative of concurrence shows the non-analytic behavior at the exceptional point, and the same is true in the case of the biorthogonal basis, which indicates that the concurrence can characterize the phase transition in this non-Hermitian system. The interesting thing is that η weakens the thermal entanglement when the system is isotropic and enhances the entanglement when the system belongs to the Ising universality class. For the one-dimensional spin chain, the magnetization and entanglement are further studied by using the two-spin cluster mean-field approximation. The results show that their variations have opposite trends with the magnetic fields. Moreover, the system exists the first-order quantum phase transitions for some anisotropic parameters in the P T -symmetry region, and the entanglement changes suddenly at the quantum phase transition point. [ABSTRACT FROM AUTHOR]

The spin dynamics of one-dimensional quantum Ising chain with random correlated magnetic fields (RCMFs) is studied at the high-temperature limit by the recursion method. Both the spin autocorrelation function and its corresponding spectral density are investigated under the circumstance of bimodal-type and Gaussian-type RCMFs. It is found that the dynamics of the system are highly dependent on the correlated mode and strength between the longitudinal and transverse magnetic fields (i.e., B x i and B z i). Due to the cooperation or synergy effect between B x i and B z i , crossovers between different dynamical behaviors can be revealed in most of the cases. In general, the dynamics of the system is dominant by the field (B x i or B z i) with a larger proportion when the RCMFs are weak. However, when the RCMFs are strong, the system tends to exhibit a disordered behavior, which manifests as a multiple-peak feature in the bimodal-type case or a broaden spectral in the Gaussian-type case. In another perspective, when the proportion of B z i is small, the central-peak behavior can be enhanced by increasing the proportion of B x i. Interestingly, when the proportion of B z i is large, the perturbation of B x i on B z i tends to excite new dynamical behavior. Our results indicate that using RCMF to manipulate the spin dynamics of the Ising system may be a new try. • The spin dynamics of quantum Ising chain with random correlated magnetic fields is studied. • The dynamical results are highly dependent on the correlated mode and strength between the longitudinal and transverse magnetic fields. • The results for the bimodal-type and Gaussian-type random correlated magnetic fields are consistent with each other. [ABSTRACT FROM AUTHOR]

The dynamics of the random Ising spin chain in coexisting transverse and longitudinal magnetic fields is studied by the recursion method. Both the spin autocorrelation function and its spectral density are investigated by numerical calculations. It is found that system’s dynamical behaviors depend on the deviation σ J of the random exchange coupling between nearest-neighbor spins and the ratio r l t of the longitudinal and the transverse fields: (i) For r l t = 0 , the system undergoes two crossovers from N independent spins precessing about the transverse magnetic field to a collective-mode behavior, and then to a central-peak behavior as σ J increases. (ii) For r l t ≠ 0 , the system may exhibit a coexistence behavior of a collective-mode one and a central-peak one. When σ J is small (or large enough), system undergoes a crossover from a coexistence behavior (or a disordered behavior) to a central-peak behavior as r l t increases. (iii) Increasing σ J depresses effects of both the transverse and the longitudinal magnetic fields. (iv) Quantum random Ising chain in coexisting magnetic fields may exhibit under-damping and critical-damping characteristics simultaneously. These results indicate that changing the external magnetic fields may control and manipulate the dynamics of the random Ising chain. [ABSTRACT FROM AUTHOR]

Quantum phase transitions (QPT) in the infinite-long Ising-XXZ diamond chain, characterized by the quantum correlations measured by the quantum discord (QD) and the entanglement of formation (EoF), are investigated exactly by the transfer-matrix method. QD and EoF are calculated numerically for different values of anisotropy parameter, external magnetic field, and temperature. It is found that the singularity of QD and EoF around quantum critical points (QCPs), especially that of their first derivatives may not only spotlight the QCPs but also depict the QPT from unentangled state in ferrimagnetic phase to an entangled state in frustrated phase or to an entangled state in the ferrimagnetic phase. [ABSTRACT FROM AUTHOR]

Using semi-classical approximation method, the Bose-Einstein condensation (BEC) of a relativistic ideal boson gas (RIBG) in random box is studied. The exact BEC transition temperature Tc and Helmholtz free energy at Tc are derived. The phase diagrams in the (Δ, T) plane are obtained, where Δ is the fluctuation of the box length and T is the temperature of the system. We find that Tc is lowered by the presence of the quenched disorder caused by the random boundary conditions. The effects of antibosons on the RIBG are also studied and it is found that the Helmholtz free energy of the system with antibosons at Tc is lower than that of the system without antibosons. This implies that the omission of antibosons always leads to a metastable state. [ABSTRACT FROM AUTHOR]

The state function entropy and its quantum thermodynamical implication for two typical dissipative systems with anomalous spectral densities are studied by investigating on their low-temperature quantum behavior. In all cases, it is found that the entropy decays quickly and vanishes as the temperature approaches zero. This reveals a good conformity with the third law of thermodynamics and provides another evidence for the validity of fundamental thermodynamical laws in the quantum dissipative region. [ABSTRACT FROM AUTHOR]

Abstract: By the concept of negativity, we investigate the thermal entanglement in the two-spin Heisenberg XXX and XXZ models in the presence of Dzyaloshinskii–Moriya interactions respectively. Through calculation, we know that for the XXZ model, the and can be used together to control the extent of entanglement and, in particular, to obtain large entanglement. The effect of spin in both models shows that it can increase the critical temperature and the negativity decreases as the spin increases. We found that the DM interaction has different effects on Fermi and Bose systems so it can not only excite entanglement but also affect the entanglement in different spin systems. [Copyright &y& Elsevier]

Employing the correlation matrix technique, the spatial distribution of thermal energy in two-dimensional triangular lattices in equilibrium, interacting with linear springs, is studied. It is found that the spatial distribution of thermal energy varies with the included angle of the springs. In addition, the average thermal energy of the longer springs is lower. Springs with different included angle and length will lead to an inhomogeneous spatial distribution of thermal energy. This suggests that the spatial distribution of thermal energy is affected by the geometrical structure of the system: the more asymmetric the geometrical structure of the system is, the more inhomogeneous is the spatial distribution of thermal energy. [ABSTRACT FROM AUTHOR]

Spin dynamics of quantum Ising system has been the subject of condensed matter physics in the past few decades. In this work, the bond-impurity effects on dynamics of the one-dimensional quantum Ising model with both transverse (B z i) and longitudinal magnetic field (LMF, B x i) was studied in the high-temperature limit by the recurrence relations method. Three cases, i.e., the LMF effect on the dynamics of the pure Ising model without impurity ( B x i ≠ 0), the weak- and strong-bond impurity effect on the dynamics of the transverse Ising model without LMF (the impurity strength J j ≠ J i , B x i = 0), and their combining effect ( J j ≠ J i , B x i ≠ 0), were investigated respectively. It is found that the dynamical behaviors of the system depend on both the impurity and the LMF. In general, the central-peak behavior (collective-mode behavior) will be enhanced (depressed) when increasing J j or B x i properly. However, when J j reaches a critical value J j c , the spin motion will be frozen, i.e., the bond impurity will act as a switch, which may turn off or turn on the spin motion. In contrast, the LMF can active the motion of the frozen spin. Therefore, the dynamical behavior of the Ising system depends on the combining effects of the impurity and the LMF. [ABSTRACT FROM AUTHOR]

In this manuscript we investigate the one-dimensional anisotropic XY model with ferromagnetic and antiferromagnetic interactions, which gives more interesting phase diagram and dynamic critical behaviors. By using quantum renormalization-group method, we find that there are three phases in the system: antiferromagnetic Ising phase ordered in " x direction", spin-fluid phase and ferromagnetic Ising phase ordered in " y direction". In order to study the dynamical critical behaviors of the system, two quantum quenching methods are used. In both cases, the concurrence, a measure of entanglement, oscillates periodically over time. It if found that in the both cases the periods are the same and can be used as a order parameter for quantum phase transitions. It is also found that there is a scaling behavior for the evolution period and a reciprocal relation for the evolution period exponent, θ and correlation length exponent, ν. [ABSTRACT FROM AUTHOR]

Abstract: Bose–Einstein condensation of two- and three-dimensional boson gases confined in the one-dimensional gravitational field is investigated. Using the semiclassical approximation method, the expressions for the BEC transition temperature, condensate fraction, heat capacity and the entropy of the system are obtained. The heat capacities of the systems with D=1, 2, 3 ( is the dimension) at the critical temperature are discussed. We find that for the 1-D and 2-D boson systems, the heat capacities are continuous, but for the 3-D case there is a gap at the critical temperature . The entropies of the systems with D=1, 2, 3 are also studied in detail. It is found that the entropies increase with the increasing of the temperature T. [Copyright &y& Elsevier]

In order to study the entanglement properties of mixed-spin systems, taking Negativity as a measure of quantum entanglement, it is studied in (1/2, 1) mixed-spin XY systems. It is found that both ferromagnetic or antiferromagnetic cases, the Negativity of systems decreases with increasing temperature and finally changes to zero smoothly. An interesting phenomenon is that the temperature T 0 (defined as the characteristic temperature) at which the Negativity becomes zero is low when the value of the crystal field parameter D is large. The relation between the thermal entanglement(T → 0) and ground-state entanglement with two and three sites is studied, respectively. It is also found that the mixed-state entanglement and the thermal entanglement at T → 0 can be well corresponding in both systems studied; but the Negativity in pure state and that in mixed state are quite different in the system with two sites. [ABSTRACT FROM AUTHOR]