Mutual thermal equilibrium in long-range Ising model using nonadditive entropy

Mutual equilibrium in long-range interacting systems which involve nonadditive energy, is effectively described in terms of entropy with a nonadditive composition rule. As an example, long-range Ising model is considered. The generality of the term having product of the system entropies is pointed out in this framework.     

Surface tension in the Ising model

We investigate the problem of a microscopic definition of the surface of separation between two phases in the special case of the 2-dimensional Ising model. We show how this leads to a definition of the surface tension which appears, in this context, as the logarithm of a partition function over a set of random surfaces. We also discuss the more general problem of defining the surface tension in an Ising ferromagnet with arbitrarily extended attractive interaction.     

Block-spins interactions in the Ising model

We investigate the interactions between block-spins in the large magnetic field region for the nearest neighbour,d-dimensional, Ising model.     

Decomposition of Ising spin of spin-S Ising model

We propose a general method by which an Ising spin of a spin-S Ising model is decomposed into Ising spins less than S. Some exactly solvable spin-S Ising models with S greater than 1/2 are obtained without using Horiguchi's condition or its extended conditions. These systems are reduced to the Ising model of spin ± 1 or an Ashkin-Teller model.     

Semi-infinite Ising model

We study the equilibrium statistical mechanics of the semi-infinite Ising model, interpreted as a model of a binary system near a wall. In particular, the wetting transition is analyzed. In dimensionsd3 and at low temperature, we prove the existence of a layering transition which is of first-order.Dedicated to Walter Thirring on his 60^th birthday     

On the uniqueness of the equilibrium state for Ising spin systems

We show that for an Ising spin system of arbitrary spin with a ferromagnetic pair interaction and a periodic external magnetic field there is a unique equilibrium state if and only if the magnetization is continuous with respect to a uniform change in the external field. Hence, if the critical temperatureT _c is defined as the temperature where the spontaneous magnetization (which is a non-increasing function of the temperature) becomes positive, then the equilibrium state is unique forT>T _c and is non-unique forT<T _c (when the external field is zero). This implies that the correlation functions have a cluster property forT>T _c .We also show that for an anti-ferromagnet consisting of two sublattices there is a unique equilibrium state if and only if the staggered magnetization is continuous with respect to a change in the staggered field.Supported in part by U.S.A.F.O.S.R. under contract F 44620-71-C-0013, P001.     

Metastability and the Ising model

We discuss a recent theorem which establishes a precise connection between (i) the approximate degeneracy of the zero eigenvalue for the generator of the Glauber dynamics of the Ising model in a small nonzero field and below the critical temperature, (ii) the existence of a partition of the configuration space into a normal region and a metastable region. This enables us to demonstrate that the recent approach to metastability of Davies and Martin may be viewed as a simple (although in some ways fairly crude) approximation to the conventional approach. We also obtain what appear to be the first results concerning the stability of metastable states under small perturbations.     

Dimers and the Ising model

We present a innovative relationship between ground states of the Ising model and dimer coverings which sheds new light on the Ising models with highly degenerate ground states and enables one to construct such models. Thanks to this relationship we also find the generating function for dimers as the appropriate limit of the free energy per spin for the Ising model.     

Semi-infinite Ising model

For the semi-infinite Ising model in two or more dimensions, we prove analyticity properties of the surface free energy and map out the phase diagram in the absence of an external magnetic field. We prove that this phase diagram contains critical lines where the parallel and/or the transverse correlation lengths diverge. The critical exponent,v _⊥, of the transverse correlation length is shown to be equal to the exponentv of the Ising model on an infinite lattice. In a second paper, these results will be used to analyze the wetting transition.     

Probabilistic characterization of the Ising model

The object of this paper is to show that Ising models can be completely characterized by the probabilistic Markov property and to derive some conclusions from this relationship.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Vacuum tunneling in the four-dimensional Ising model

In the broken phase of the four-dimensional Ising model tunneling between the two degenerate minima of the effective potential takes place in a finite volume. We study this phenomenon numerically. The energies of the lowest zero momentum states are determined on both sides of the phase transition and their different correspondence to particle states in the infinite-volume limit is discussed. A Z₂-invariant definition of the field expectation value and susceptibility is exploited for calculation of the quantities in finite volumes.     

Methods for reconstructing equilibrium plasma configurations in the Globus-M spherical tokamak

A magnetic diagnostics allowing one to reliably reconstruct equilibrium plasma configurations in a tokamak over a wide range of operating parameters is developed. The accuracy of determining the geometrical parameters and thermal energy of the tokamak plasma is analyzed in detail. The experimental data obtained in the Globus-M tokamak are processed the with help of the EFIT code. The influence of the plasma configuration on the intensity of the main impurity lines is investigated.     

Ising model in the high density limit

It is proved that the free energy per spin in the thermodynamic limit of an Ising model on a lattice with coordination numberz approaches the classical Curie-Weiss free energy in the limitz→∞. The infinite spacial dimension limit of nearest neighbour lattice models is a special case of this result.     

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。     

Superparamagnetism in the 1D Ising model

The temperature dependence of the order parameter (〈M ²〉, the mean-square spin excess per spin) for a system with a finite number of spins of the 1D Ising model was investigated. It was shown that there is a nonzero temperature T _s below which 〈M ²〉 rapidly tends to unity. The analogy between the 1D ensemble of a finite number of spins and a system of superparamagnetic particles is discussed.     

Interface delocalization in the three-dimensional Ising model

The interface delocalization in the three-dimensional Ising model is studied by real-space renormalization group methods. The first-order cumulant expansion approximation is used. Defect free energies for a boundary plane of defects and an internal plane of defects are calculated in the whole temperature region. The phase diagrams are also obtained. The method and the model analyzed may give a correct phase diagram only in the regime of continuous interface delocalization. The interface delocalization is obtained for the boundary defect and also for the internal defect if the systems on two sides of the internal defect plane have a different degree of order. The delocalization transition does not occur in the case of the internal defect plane between two equally ordered systems.