Dynamic Critical Behavior of 2D X-Y Model on a Random Lattice from Cluster Update Monte Carlo

We performed a numerical simulation of X-Y model on the two-dimensional random lattice using cluster update algorithm. The critical region was found around β≈1.0 by the peaks in the specific heat and the susceptibility. The autocorrelation in energy and the square of magnetization was also calculated. The results show that the critical slowing down was greatly reduced.     

Berezinskii-Kosterlitz-Thouless Transition in a Two-Dimensional Random-Bond XY Model on a Square Lattice

We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown that the two kinds of disorders lead to similar thermodynamic behaviors if their variances take the same value. This result implies that the variance can be chosen as a characteristic parameter to evaluate the strength of the randomness. In addition, the Berezinskii-Kosterlitz-Thouless transition temperature decreases as the variance increases and the transition can even be destroyed as long as the disorder is strong enough.     

Phase Diagram of XY Model with Nematic Coupling on the Simple Cubic Lattice

Using cluster Monte Carlo method,we numerically investigate the criticality in the XY model with nematic coupling on the simple cubic lattice.We determine critical lines belong to the three-dimensional XY universality class in variable of θ(2θ) between the XY-ferromagnetic(nematic) and disordered states.Furthermore,the phase transition between the XY-ferromagnetic and the nematic states is found to be in the three-dimensional Ising universality class.The critical points are determined from the intersections of Binder ratios for various system sizes.With two sets of critical points obtained,we finally construct the phase diagram on the-J plane.     

Phase Transition for the Ising Model on the Critical Lorentzian Triangulation

The ferromagnetic Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of the Peierls contour method. The critical temperature is shown to be constant a.s.     

The Critical Behavior of the Ising Model on Union Jack Lattice

In this paper, we have investigated the critical behavior of the ferromagnetic Ising model on union jack lattice. The model is equivalent to the eight-vertex model which can be solved as a free fermion model with the free fermion approximation. The critical exponents have been obtained as aα = α = 0, β = β'= 0.125, γ = γ' = 0.875 and δ = δ' = 8.     

From Continuous to First Order Phase Transition in a Generalized XY Model

A generalized XY model with interaction V(θ) = 2 J{1 - [cos² (θ/2)]^p2} is studied by Monte Carlo renormalization group method on two-dimensional random triangle lattice. For p = √2, a line of fixed points has been found. It characterizes that there is a Kosterlitz-Thouless phase transition. For p = 2, a first order phase transition has been found. Both of them show the relationship between the nature of phase transition and the class of interactions.     

Critical Behavior for Maximal Flows on the Cubic Lattice

Let F ₀ and F _m be the top and bottom faces of the box [0, k]×[0, l]×[0, m] in Z ³. To each edge e in the box, we assign an i.i.d. nonnegative random variable t(e) representing the flow capacity of e. Denote by Φ _k, l, m the maximal flow from F ₀ to F _m in the box. Let p _c denote the critical value for bond percolation on Z ³. It is known that Φ _k, l, m is asymptotically proportional to the area of F ₀ as m, k, l→∞, when the probability that t(e)>0 exceeds p _c , but is of lower order if the probability is strictly less than p _c . Here we consider the critical case where the probability that t(e)>0 is exactly equal to p _c , and prove that $$\mathop {{\text{lim}}}\limits_{k,l,m \to \infty } \frac{1}{{kl}}\Phi _{k,l,m} = 0{\text{ a}}{\text{.s and in }}L_1 $$ The limiting behavior of related to surfaces on Z ³ are also considered in this paper.     

Critical Behavior of the Annealed Ising Model on Random Regular Graphs

In Giardinà et al. (ALEA Lat Am J Probab Math Stat 13(1):121–161, 2016), the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in Can (Annealed limit theorems for the Ising model on random regular graphs, arXiv:1701.08639, 2017), we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem stating that the magnetization scaled by \(n^{3/4}\) converges to a specific random variable, with n the number of vertices of random regular graphs.     

Influence of Inhomogeneity on Critical Behavior of Earthquake Model on Random Graph

We consider the earthquake model on a random graph. A detailed analysis of the probability distribution of the size of the avalanches will be given. The model with different inhomogeneities is studied in order to compare the critical behavior of different systems. The results indicate that with the increase of the inhomogeneities, the avalanche exponents reduce, i.e., the different numbers of defects cause different critical behaviors of the system. This is virtually ascribed to the dynamical perturbation.     

Influence of Inhomogeneity on Critical Behavior of Earthquake Model on Random Graph

We consider the earthquake model on a random graph. A detailed analysis of the probability distribution of the size of the avalanches will be given. The model with different inhomogeneities is studied in order to compare the critical behavior of different systems. The results indicate that with the increase of the inhomogeneities, the avalanche exponents reduce, i.e., the different numbers of defects cause different critical behaviors of the system. This is virtually ascribed to the dynamical perturbation.     

A Strict Inequality for the Random Triangle Model

The random triangle model on a graph G, is a random graph model where the usual i.i.d. measure is perturbed by a factor q ^t(), where q1 is a constant, and t() is the number of triangles in the random subgraph . Here we consider the case where G is the usual two-dimensional triangular lattice, for which there exists a percolation threshold p _c (q) such that the probability of getting an infinite connected component of retained edges is 0 for p<p _c (q), and 1 for p>p _c (q). It has previously been shown that p _c (q) is a decreasing function of q. Here we strengthen this by showing that p _c (q) is strictly decreasing. This confirms a conjecture by Häggström and Jonasson.     

Thermodynamic Phase Transition and Critical Behavior of a Spherical Symmetric Black Hole

In this paper, we builded the thermodynamics model of black hole based on the method of York. We obtained the reduced temperature reciprocal function using the action of the system. We studied the phase structure of black holes and Hawking-Page phase transition. We obtained the first order phase transition and critical values of black hole in Rerssner-NordstrÖm space time. The results showed that only when two-phase coexistence appeared only when |q| < |q_c|.     

Critical Behavior of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior.     

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〉.     

Phase Transitions and the Critical Properties of the Heisenberg Model on a Body-Centered Cubic Lattice

Physics of the Solid State - The Monte Carlo replica technique is used to study phase transitions and the thermodynamic and critical properties of the three-dimensional Heisenberg antiferromagnetic...     

PNJL模型下手征相变的临界指数

在PNJL模型下研究了临界点和旋节线边界上的临界指数。计算表明四个标准的临界指数$\alpha,\,\beta,\,\gamma,\,\delta$在 平均场近似下与朗道-金斯堡理论的预言一致。重子数涨落分布峰态的临界指数$\eta(\approx2)$大于偏态的 临界指数$\zeta(\approx1)$,这表明,如果在重离子碰撞实验中可以达到临界区域,峰态的测量比偏态的测量更加敏感。计算结果还表明,偏态(峰态)在旋节线边界上的临界指数与在临界点的临界指数具有相同的发散强度。根据重子数在不稳定相和亚稳相的剧烈涨落及峰态和偏态在旋节线边界上发散的特点,在将来的实验中用于鉴别一阶相变的信号在一定程度上会被干扰,一些偏离标准一阶相变的信号或许会在观测中发现。     

Quantum Correlations in Infinite XY Spin-1/2 Chains and Quantum Phase Transition

We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.