Finite-size scaling of the three-state Potts model on a simple cubic lattice

Finite-size scaling is studied for the three-state Potts model on a simple cubic lattice. We show that the specific heat and the magnetic susceptibility scale accurately as the volume. The correlation length exhibits behaviors expected for a genuine first-order transition; the one extracted from the unsubtracted correlation function shows a characteristic finite-size behavior, whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point.     

Monte Carlo simulations of conformal theory predictions for the three-state Potts model

The critical properties of the three-state Potts model are investigated using Monte Carlo simulations. Special interest is given to the measurement of three-point correlation functions and associated universal objects, i.e., structure constants. The results agree well with predictions coming from conformal field theory, confirming, for this example, the correctness of the Coulomb gas formalism and the bootstrap method.     

Propagation of order in the dilute antiferromagnetic three-state Potts model

A recent analysis of the propagation of order in a dilute 3-state Potts antiferromagnetic model on a triangular lattice at zero temperature by Adleret al. has shown the importance of nonlocality in the propagation of order. We study a linearized continuous version of this model, which can be mapped onto three independent percolation problems. We discuss the respective roles of nonlocality and nonlinearity, in particular in connection with central-force percolation.     

自对耦无序分布随机链Potts模型的临界普适性研究

以蒙特卡罗模拟方法对自对耦分布二维随机链q态Potts模型的短时临界行为进行了数值研究.利用初始非平衡演化阶段存在的普适幂指数和有限体积标度行为，数值模拟了在不同形式随机分布时q＝3和q＝8态Potts模型磁临界指数η和动力学临界指数z.计算结果发现η不依赖于自对偶无序分布的具体形式， 从而以数值方法给出了一个关于淬火掺杂自旋系统的临界普适行为的验证. 关键词： 随机链Potts模型 动力学蒙特卡罗模拟 临界普适性     

Finite-size effects and phase transition in the three-dimensional three-state Potts model

The three-state Potts model in three dimensions is studied by Monte Carlo and finite-size scaling techniques. Using a histogram method recently proposed by Ferrenberg and Swendsen, the finite-size dependence for the maximum of the specific heat is found to scale with the volume of the system, indicating that the phase transition is of first order. The value of the latent heat per spin and the correlation length at the transition are estimated.     

Study of cluster fluctuations in the two-dimensional q-state Potts model

The two-dimensional Potts model with 2 to 10 states is studied using a cluster algorithm to calculate fluctuations in cluster size as well as commonly used quantities like equilibrium averages and the histograms for energy and the order parameter. Results provide information about the variation of cluster sizes depending on the temperature and the number of states. They also give evidence for first-order transition when energy and the order parameter related measurables are inconclusive on small size lattices.     

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Critical properties of XY model dimensional layered magnetic on two- films

Using Monte Carlo simulations, we have investigated the classical $XY$ model on triangular lattices of ultra-thin film structures with middle ferromagnetic layers sandwiched between two antiferromagnetic layers. The internal energy, the specific heat, the chirality and the chiral susceptibility are calculated in order to clarify phase transitions and critical phenomena. From the finite-size scaling analyses, the values of critical exponents are determined. In a range of interaction parameters, we find that the chirality steeply goes up as temperature increases in a temperature range; correspondingly the value of a critical exponent for this change is estimated.     

Critical exponents of Manhattan Hamiltonian walks in two dimensions,from Potts andO(n) models

We consider a set of Hamiltonian circuits filling a Manhattan lattice, i.e., a square lattice with alternating traffic regulation. We show that the generating function (with fugacityz) of this set is identical to the critical partition function of aq-state Potts model on an unoriented square lattice withq ^1/2 =z. The set of critical exponents governing correlations of Hamiltonian circuits is derived using a Coulomb gas technique. These exponents are also found to be those of an O(n) vector model in the low-temperature phase withn =q ^1/2 =z. The critical exponents in the limitz = 0 are then those of spanning trees (q= 0) and of dense polymers (n=0,T < T_c), corresponding to a conformal theory with central chargeC = –2. This shows that the Manhattan orientation and the Hamiltonian constraint of filling all the lattice are irrelevant for the infrared critical properties of Hamiltonian walks.     

Height Representation,Critical Exponents,and Ergodicity in the Four-State Triangular Potts Antiferromagnet

We study the four-state antiferromagnetic Potts model on the triangular lattice. We show that the model has six types of defects which diffuse and annihilate according to certain conservation laws consistent with their having a vector-valued topological charge. Using the properties of these defects, we deduce a (2+2)-dimensional height representation for the model and hence show that the model is equivalent to the three-state Potts antiferromagnet on the Kagomé lattice and to bond-coloring models on the triangular and honeycomb lattices. We also calculate critical exponents for the ground-state ensemble of the model. We find that the exponents governing the spin–spin correlation function and spin fluctuations violate the Fisher scaling law because of constraints on path length which increase the effective wavelength of the spin operator on the height lattice. We confirm our predictions by extensive Monte Carlo simulations of the model using the Wang–Swendsen–Kotecký cluster algorithm. Although this algorithm is not ergodic on lattices with toroidal boundary conditions, we prove that it is ergodic on lattices whose topology has no noncontractible loops of infinite order, such as the projective plane. To guard against biases introduced by lack of ergodicity, we perform our simulations on both the torus and the projective plane.     

Static and dynamic critical phenomena of the two-dimensionalq-state Potts model

Theq-state Potts model on the square lattice is studied by Monte Carlo simulation forq=3, 4, 5, 6. Very good agreement is obtained with exact results of Kiharaet al. and Baxter for energy and free energy at the critical point. Critical exponent estimates forq=3 are0.4,0.1,1.45, in rough agreement with high-temperature series extrapolation and real space renormalization-group methods. The transition forq=5, 6 is found to be a very weakly first-order transition, i.e., pronounced pseudocritical phenomena occur, specific heat, susceptibility, etc. (nearly) diverge at the first-order transition temperature. Dynamics is associated to the model in the same way as for the kinetic Ising model, and the nonlinear slowing down of the order parameter and of the energy is studied. The dynamic exponent is estimated to be (=zv)1.9. Within our accuracy noq dependence is detected. The relaxation is found to be consistent with dynamic scaling predictions, and dynamic scaling functions associated with the nonlinear relaxation are estimated.     

Critical wetting in the square Ising model with a boundary field

The Ising square lattice with nearest-neighbor exchangeJ>0 and a free surface at which a boundary magnetic fieldH ₁ acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.Alexander von Humboldt-Fellow     

外磁场下XY模型中两量子位热纠缠的性质及其调控研究

在海森堡XY模型中,为了统一研究均匀磁场和非均匀磁场对系统热纠缠的影响,在两个量子位分别施加独立可控的外磁场(B+b)和(B-b). 发现在均匀磁场和低温条件下的纠缠度有一个稳定的平台区并发生纠缠突变. 控制磁场不均匀度b和选择合适的材料就可以获得最有利的纠缠,并大大提高系统退纠缠的临界温度T_c. 调节磁场的B值,可以在更宽的温度范围内实现此体系的纠缠开关. 关键词： 热纠缠度 密度矩阵 XY模型')" href="#">XY模型     

Interfacial roughness and temperature effects on exchange bias properties in coupled ferromagnetic/antiferromagnetic bilayers

Monte Carlo simulations have been used to study the relationship between the exchange bias properties and the interface roughness in coupled ferromagnetic/antiferromagnetic (FM/AFM) films of classical Heisenberg spins. It is shown that the variation of the exchange bias field versus the AFM anisotropy strongly depends on the FM/AFM interface. Unlike the flat interface, a non-monotonic dependence is observed for the roughest FM/AFM interface. This is explained by canted magnetic configurations at the FM/AFM interface, which appear after the first reversal due to the magnetic frustration. The temperature dependence of the exchange field is also dependent on the roughness. While the exchange field is roughly constant for the flat interface, a decrease is observed for the roughest interface as the temperature increases. This has been interpreted as a significant decrease of the effective coupling between the FM and the AFM due to the disordering of the moments at the FM/AFM interface because of the combination of magnetic frustration and temperature activation.     

On the dynamics and ergodic properties of theXY model

The return to equilibrium is investigated for one-dimensional (one-sided) chain of theXY model. The initial state is taken to be the Gibbs state for the sum of the Hamiltonian for theXY model of lengthN and a perturbation by a uniform magnetic field acting on the firstn sites. The time evolution under the unperturbedXY model Hamiltonian is studied for the expectation value of the average magnetization of the same firstn sites in the infinitely extended system (i.e., after taking the limitN). It is found that the return to equilibrium occurs for a finite-size perturbation (i.e., for a fixedn), while it does not occur for an infinite-size perturbation (i.e., the limit n is taken simultaneously as N). A certain twisted asymptotic Abelian property of theXY model is shown and used as a technical tool.     

小体积比两相分离早期过程的三维格子气模型研究

采用Monte Carlo模拟方法研究了小体积比三维格子气模型中的相分离过程, 比较了sc, fcc, bcc 等3种晶格类型和T/T_c=0.45–0.85等 5个相对温度的系统演化行为, 计算了系统的结构因子函数, 发现结构因子在相分离早期不满足标度关系, 生长指数等于1/6, 小于经典Lifshitz-Slyozov理论的值. 关键词： 格子气模型 相分离过程 Monte Carlo模拟 生长律     

One-dimensionalXY model: Ergodic properties and hydrodynamic limit

We prove theorems on convergence to a stationary state in the course of time for the one-dimensionalXY model and its generalizations. The key point is the well-known Jordan-Wigner transformation, which maps theXY dynamics onto a group of Bogoliubov transformations on the CARC ^*-algebra overZ ¹. The role of stationary states for Bogoliubov transformations is played by quasifree states and for theXY model by their inverse images with respect to the Jordan-Wigner transformation. The hydrodynamic limit for the one-dimensionalXY model is also considered. By using the Jordan-Wigner transformation one reduces the problem to that of constructing the hydrodynamic limit for the group of Bogoliubov transformations. As a result, we obtain an independent motion of normal modes, which is described by a hyperbolic linear differential equation of second order. For theXX model this equation reduces to a first-order transfer equation.