Phase Diagram of the Antiferromagnetic Heisenberg Model on a Cubic Lattice

Phase transitions in the antiferromagnetic Heisenberg model on a cubic lattice with intralayer next-nearest neighbor interactions are studied using the replica Monte Carlo algorithm. The magnitude of next-nearest neighbor interactions varies in the range of 0.0 ≤ r ≤ 1.0. The characteristics of the phase transitions are analyzed by the histogram and Binder cumulant techniques. The phase diagram relating the transition temperature and the magnitude of next-nearest neighbor interactions is constructed. It is shown that a second order phase transition occurs in the r range under study. In this model, it is found that the intralayer next-nearest neighbor interactions do not change the order of the phase transition.

     

Phase Fluctuations in the ABC Model

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of L sites, the steady state profiles move on a microscopic time scale of order L ³. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations.     

The Phase Diagram of a Spin Glass Model

A spin glass problem on a Cayley tree with ferromagnetic interactions is solved rigorously. Using a level-I large deviation argument together with the martingale approach used by Buffet, Patrick and Pulé,⁽¹⁾ explicit expressions for the free energy are derived in different regions of the phase diagram. It is found that there are four phases: a paramagnetic phase, a spin-glass phase, a ferromagnetic phase and a mixed phase. The nature of the phase diagram depends on the power with which the ferromagnetic term occurs in the Hamiltonian.     

The Phase Diagram of the Quantum Curie-Weiss Model

This paper studies a generalization of the Curie-Weiss model (the Ising model on a complete graph) to quantum mechanics. Using a natural probabilistic representation of this model, we give a complete picture of the phase diagram of the model in the parameters of inverse temperature and transverse field strength. Further analysis computes the critical exponent for the vanishing of the order parameter in the approach to the critical curve and gives useful stability properties for a variational problem associated with the representation.     

Phase Diagram for Ashkin-Teller Model on Bethe Lattice

Using the recursion method, we study the phase transitions of the Ashkin-Teller model on the Bethe lattice, restricting ourselves to the case of ferromagnetic interactions. The isotropic Ashkin-Teller model and the anisotropic one are respectively investigated, and exact expressions for the free energy and the magnetization are obtained. It can be found that each of the three varieties of phase diagrams, for the anisotropic Ashkin-Teller model, consists of four phases, i.e., the fully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Ferro, and two partially ordered ferromagnetic phases 〈σ〉and 〈σs〉, while the phase diagram, for the isotropic Ashkin-Teller model, contains three phases, i.e., the fully disordered paramagnetic phase Para, the fully ordered ferromagnetic phase Baxter Phase, and the partially ordered ferromagnetic phase 〈σs〉.     

Drift of Phase Fluctuations in the ABC Model

In a recent work, Bodineau and Derrida analyzed the phase fluctuations in the ABC model. In particular, they computed the asymptotic variance and, on the basis of numerical simulations, they conjectured the presence of a drift, which they guessed to be an antisymmetric function of the three densities. By assuming the validity of the fluctuating hydrodynamic approximation, we prove the presence of such a drift, providing an analytical expression for it. This expression is then shown to be an antisymmetric function of the three densities. The antisymmetry of the drift can also be inferred from a symmetry property of the underlying microscopic dynamics.     

Phase Diagram of One-Dimensional Fermi Gas Model

The phase diagrams of one-dimensional g-ology model are studied. The known results of the XXZ spin 1/2 chain model are applied to extending the solutions to the massless range where the method of Gaussian wave functional is insufficient. The response functions of CDW, SDW, SS and TS are computed as temperature T→0.     

改进的PNJL模型下QCD的相图

Polyakov-Nambu-Jona-Lasinio（PNJL）模型是研究强相互作用物质性质的使用最为广泛的有效模型之一。在PNJL模型的基础上考虑了手征凝聚和Polyakov圈之间的纠缠作用,并且引入了化学势修正的Polyakov有效势,由此得到了化学势依赖的entangled PNJL（μEPNJL）模型。在平均场框架下的计算结果表明:相较于原始的PNJL模型,由μEPNJL模型计算得到的临界点（CEP）朝着温度更高、化学势更小处移动,并且手征对称性恢复相变和退禁闭相变在较大的化学势范围内都重合得很好。通过与STAR合作组在相对论重离子对撞机（RHIC）上进行的净质子数分布的测量结果相比,可以发现,通过适当的参数调节,由μEPNJL模型计算得到的CEP更加靠近实验预言的CEP可能存在的区域。Polyakov-Nambu-Jona-Lasinio (PNJL) model is one of the most popular effective quark models to investigate the properties of strongly interacting matter. Based on the PNJL model, we consider the entanglement interactions between the chiral condensate and Polyakov-loop, as well as the chemical potential modification of Polyakov-loop potential simultaneously, which is named μEPNJL model. Compared with the original PNJL model, the calculations in the mean field approximation show that the critical end point (CEP) given in the μEPNJL model moves towards higher temperature and smaller chemical potential in the T-μ phase diagram. Besides, the chiral symmetry restoration and deconfinement phase transition coincide well in a wide range of chemical potential. Comparing our calculations with the measurement of the moments of net-proton multiplicity distributions at Relativistic Heavy-Ion Collider (RHIC) by STAR Collaboration, we find that the CEP given by μEPNJL model can be closer to the range predicted by the experiment through appropriate parameter adjustment.     

Phase Diagram of a Two-Species Lattice Model with a Linear Instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy ( Phys . Rev. Lett ., 79 , 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.     

The Improved Subregular Model and the Phase Diagram of a Binary System

In thia paper an improved subregular model is proposed. Using the thermodynamic theory the equations describing liquid-solid phase equilibrium curve are obtained. For some typical phase diagrams of a binary system we give their predictive criteria of the phase diagram type. We enumerate 4 binary alkali halide systems, their phase diagrams are calculated respectively, this improved model is tested. The results calculated show that the agreement between the theoretical phase diagram and its corresponding experimental points is good.     

Phase Transition in a Generalized Eden Growth Model on a Tree

We study analytically the late time statistics of the number of particles in an Eden growth model on a tree. In this model, a cluster grows in continuous time on a binary Cayley tree, starting from the root, by absorbing new particles at the empty perimeter sites at a rate proportional to c ^−l where c is a positive parameter and l is the distance of the perimeter site from the root. For c=1, this model corresponds to random binary search trees and for c=2 it corresponds to digital search trees in computer science. By introducing a backward Fokker-Planck approach, we calculate the mean and the variance of the number of particles at large times and show that the variance undergoes a ‘phase transition’ at a critical value . While for the variance is proportional to the mean and the distribution is normal, for the variance is anomalously large and the distribution is non-Gaussian due to the appearance of extreme fluctuations. The model is generalized to one where growth occurs on a tree with m branches and, in this more general case, we show that the critical point occurs at .     

Phase Diagram and Ground State of a Decorated Ising Model on a Cubic Lattice

Journal of Experimental and Theoretical Physics - The static critical behavior of a three-dimensional decorated Ising model on a cubic lattice is investigated by the methods of computational...     

Geometric Phase in a Generalized Time-Dependent Jaynes-Cummings Model

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Jaynes-Cummings model. It is found that the geometric phases in a cycle case have nothing to do with the frequency of the electromagnetic wave, the energy difference between two levels of the atom, and the coupling strength between the atom and the light field.     

Geometric Phase in a Generalized Time-Dependent Karassiov-Klimov Model

By using of the invariant theory, we have studied the generalized time-dependent Karassiov-Klimov model, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

On the Phase Diagram of the 1D Hubbard Model

The conditions for the emergence of inhomogeneous states are investigated from analysis of the equation of state. It is assumed that Hubbard energy U > t, i.e., corresponds to the conditions of strong electron–electron correlations. The magnetic phase diagram is obtained in a wide range of electron concentrations corresponding to the lower Hubbard band.     

A Model Study of the Chiral Phase Diagram of QCD

In this paper we study the chiral phase transition of QCD at finite temperature and density by using the rank-2 confining separable gluon propagator model in the framework of Dyson–Schwinger Equations. The critical end point is located at (T _CEP , μ _CEP ) = (69, 270.3 MeV). It is also found that the first order phase transition might not end at one point, but experiences a two-phase coexisting meta-stable state. A comparison with the results in the previous literature is given.     

Geometric Phase in a Generalized Time-Dependent Double-Boson Interaction Model

By using of the invariant theory and the large quantum numbers approximation, we have studied a generalized time-dependent double-Boson interaction model, the dynamical and geometric phases are given, respectively. The Aharonov-Anandan phase is also obtained under the cyclical evolution.     

Phase Diagram of Random Field Spin-S Ising Model with a Transverse Field

Random field spin-S Ising model with a transverse field has been studied by making use of the pair approximation with the discretized path-integral representation, and an analytical expression of second-order phase transition is derived for all the symmetric probability distributions of (longitudinal) random fields. The phase diagrams at T = 0 are obtained, and the conditions for existence of tricritical points are examined for an arbitrary number of nearest-neighbor spins.     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method.The bond-alternative effects on its ground-state phase diagram are discussed in detail.Once the bond alternation is taken into account,the antiferromagnetic phase (Δ 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order.The QPT is shown to be second-order,and the whole phase diagram is provided.For the ferromagnetic phase region (Δ-1),the critical point r c always equals 1 (independent of Δ),and the QPT for this case is shown to be first-order.The dimerized Heisenberg model is also discussed,and two disordered phases can be distinguished by with or without nonlocal string orders.Both the bipartite entanglement and the fidelity per site,as two kinds of model-independent measures,are capable of describing all the QPTs in such a quantum model.