On the exact identities for Ising model with arbitrary spin

Adam Lipowski, Masuo Suzuki

Semen I Kuchanov, М. А. Алиев

In the limit of the strong magnetic field , the closed hierarchy of kinetic equations for correlation functions of an arbitrary order is derived for a one-dimensional kinetic Ising model. This hierarchy allows asymptotically exact solution in quadratures. For the first time the closed set of equation for generating functions of the domain distribution of the identically oriented spins have been obtained. The relations between kinetic parameters that make it possible to find exact solutions in quadratures are indicated.

Terufumi Yokota

Alexey I. Proshkin, Felix A. Kassan-Ogly

We investigated the Ising model on a linear chain with arbitrary spin including interactions between nearest and next-nearest neighbors in an applied magnetic field. A series of exact solutions and formulas for frustration fields, magnetizations and entropies at these fields at T→0 are found.

A. Elkouraychi, M. Saber, J.W. Tucker

Michael Ellis Fisher

The "star-triangle" and "decoration" transformations are generalized so as to apply to arbitrary mechanical systems coupled to the spins of a standard Ising net. This leads to exact solutions for further plane Ising nets and also for lattices in which the spins on alternate sites have a magnitude greater than $S=\frac{1}{2}$. A general class of antiferromagnetic Ising models is constructed; exact closed expressions can be derived for all the thermodynamic and magnetic properties of these models in an arbitrary magnetic field.The magnetizations and susceptibilities of Ising nets in which different spins have different magnetic moments are investigated and a valuable relation between the susceptibilities of the honeycomb and triangular lattices is derived. It is shown how correlation functions involving a given spin can be expressed in terms of correlations involving the nearest-neighbor spins instead.