On the Swendsen-Wang dynamics. II. Critical droplets and homogeneous nucleation at low temperature for the two-dimensional Ising model

We consider the Swendsen-Wang dynamics for the two-dimensional Ising model at low temperature in the presence of a small negative magnetic fieldh and with plus boundary conditions at the boundary of an arbitrarily large square. We analyze in detail the tunneling from the metastable phase to the stable one. In particular, we obtain an upper bound on the tunneling timet by explicitly constructing paths in the space of spin configurations that drive the system from the metastable phase to the stable one. In our analysis the transition takes place through the formation of droplets of the right phase inside the wrong one with side greater than a certain critical valuel _c . The values of the tunneling time and ofl _c coincide with those found for a single-spin-flip dynamics in finite volume by Jordao-Neves and Schonmann.     

Non-Hermitian Ising model at finite temperature

As a very simple model, the Ising model plays an important role in statistical physics. In the paper,with the help of quantum Liouvillian statistical theory, we study the one-dimensional nonHermitian Ising model at finite temperature and give its analytical solutions. We find that the nonHermitian Ising model shows quite different properties from those of its Hermitian counterpart. For example, the ‘pseudo-phase transition’ is explored between the ‘topological’ phase and the ‘nontopological’ pha...     

Probability distribution of random paths in the Ising model at low temperature

Communications in Mathematical Physics - The random walk representation of then-dimensional Ising model exhibits the 2-point correlation function 〈σ(x) σ(y)〉 as a sum of...     

Approximate calculations for the two-dimensional Ising model

A self-consistent molecular field approximation for the two-dimensional, square-lattice Ising model is used to calculate the energy and magnetization. Agreement with the exact calculations is good except near the critical temperature, which differs from the exact critical temperature by 4%. The specific heat has no anomalous behavior asT approachesT _c from above, and the magnetization follows the incorrect Weiss (T _c-T)^1/2 law asT approachesT _c from below.     

Boundary conditions and correlation functions in the ν-dimensional Ising model at low temperature

The boundary condition dependence of the correlation functions in a phase transition region of the thermodynamic parameters is of great importance to understand the character and properties of the phase transition itself. In this paper we study the boundary condition dependence of certain correlation functions in the Ising model at low temperature.     

New results for the susceptibility of the two-dimensional Ising model at criticality

We report several new results for the susceptibility of the two-dimensional Ising model in the critical region including the exact evaluation of the constant (first regular term) in the asymptotic expansion near T_c for the ferromagnetic case.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

Partition function zeros for the two-dimensional Ising model

The distribution of complex temperature zeros of the partition function of the two-dimensional Ising model in the absence of a magnetic field is investigated. For anisotropic square and triangular lattices the distribution function is two-dimensional and satisfies a partial differential equation derived from a generalized scaling theory. Corresponding results for the isotropic square, triangular and honeycomb lattices are also presented.     

Ising model on mixed two-dimensional lattices

We inform results on physical and topological magnitudes related to the ground level of Ising model on mixed two-dimensional lattices of coordination numbers 4 (Kagomé lattices) and 5 (five-point star lattices). We consider little clusters of size N, where N represents the total number of spins, subject to periodic boundary conditions. On these systems we randomly distribute ±J nearest-neighbor interactions (+J: antiferromagnetic, −J: ferromagnetic (F)). Concentration x of F interactions is varied in the interval (0,1). Two different methods are used to obtain results reported here. First, a numerical method related to multiple replicas. Second, an analytical method based on probabilistic analysis of flat and curved plaquettes. Both methods are complementary to each other. Initially, this study is restricted to calculate frustration of plaquettes and bonds, energy and bond order parameter at T=0. The results of magnitudes informed here are compared with the similar ones obtained for honeycomb, square and triangular lattices.     

A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Analyticity of correlation functions for the two-dimensional Ising model

Analyticity of correlation functions for the two-dimensional Ising model as a function of the inverse temperature except for the singularity at the critical temperature is proved. A crucial step is the establishment of the correspondence between extremal equilibrium states of the model and pure ground states of a one-dimensional spin system below the critical temperatureT _c . An exact decay rate of the clustering property along axes is also determined for allTT _c .     

An upper bound on the critical temperature for a continuous system with short-range interaction

A classical gas with short-range interaction in the grand canonical ensemble is studied. Ifp(, z) denotes the thermodynamic pressure at inverse temperature and activityz, then it follows from the Mayer expansion thatp(, z) is infinitely differentiable provided andz are sufficiently small. Here it is shown that there exists ₀>0 such thatp(, z) is infinitely differentiable if< ₀ andz>0. One can interpret this result as saying that ( ₀)^–1 is an upper bound on the critical temperature for the system.     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点.本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究.系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长.通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界...     

Heat conduction in a two-dimensional Ising model

A cylindrical Ising model between thermostats is used to explore the heat conduction for any temperature interval. The standard Q2R and Creutz dynamics, previously used by Saito, Takesue and Miyashita, fail below the critical temperature, limiting the analysis to high temperatures intervals. We introduce improved dynamics by removing limitations due to the chessboard-like refresh, and by supplementing the Q2R rule with Kadanoff-Swift moves. These new dynamics not only prove highly efficient in recovering old results in their domains of validity, but also allow exploration of steady heat transport between two arbitrary temperatures, i.e. very far from equilibrium. From an ansatz avoiding references to quasi equilibrium or to local temperature, and from comparison with numerical simulations, we can consistently define a generalized diffusivity. Its dependence on the energy density may be evaluated without any recourse to the Green-Kubo formula.     

二维伊辛模型的畴壁动力学

表面可以改变纳米磁性薄膜的结构和相变温度,畴壁动力学由此成为研究的重点。本文采用动力学蒙特卡罗模拟方法,对二维Ising模型磁畴界面的非平衡动力学展开数值研究。系统初态设为半正半负,即由完全有序但自旋取向完全相反的两部分组成,其间的磁畴壁随时间生长。通过对磁化标度形式的分析,发现畴壁内外的动力学标度形式虽然相同,但临界指数在数值上却存在很大差异,相差一个 =1,这是由初始条件导致的。     

低温下二维绝缘铁磁体的磁振子寿命

在二维正方绝缘铁磁系统基础上建立了一个磁振子-声子相互作用模型. 利用格林函数方法研究了磁振子-声子相互作用下的二维绝缘铁磁体的磁振子衰减(即-ImΣ^*(1)(k)), 计算了布里渊区的主要对称点线上的-ImΣ^*(1)(k).发现在布里渊区边界区域磁振子衰减很明显, 但小波矢区(k_xa/π＜0.22附近)磁振子衰减非常弱, 而且温度很低时磁振子衰减有极大值. 比较了纵向声子与横向声子对磁振子衰减的影响, 也讨论了各项参数的变化对磁振子衰减的影响. 根据关系式-Im^*(1)(k)=/(2τ)可以对磁振子寿命进行判断. 关键词： 磁振子-声子相互作用 磁振子衰减 铁磁体 磁振子寿命     

Magnetization at corners in two-dimensional Ising models

We investigate the corner spin magnetization of two-dimensional ferromagnetic Ising models in various wedge geometries. Results are obtained for triangular and square lattices by numerical studies on finite wedges using the star-triangle transformation, as well as analytic calculations using corner transfer matrices and a fermionic representation of the row-to-row transfer matrix. The corner magnetizations vanish at the bulk critical temperature T_c with an exponent _c differing from the bulk exponent. For isotropic systems with free edges we find that _c is given simply by _c =/2, where is the angle at the corner. For apex magnetizations of conical lattices we obtain the strikingly similar result _a=/4. These formulas apply equally well to anisotropic lattices if the angle is interpreted as an effective angle, ^eff, determined by the relative strengths of the interactions.     

A Remark on High Temperature Polymer Expansion for Lattice Systems with Infinite Range Pair Interactions

We consider the standard high temperature-small activity polymer expansion for lattice spin systems and show how, in many cases using a tree graph equality, various classical results may be improved in some cases or at least proved in a much simpler way.