One-Dimensional Ising Model with Arbitrary Spin

J. Szṅajd

Norikiyo Uryû, Mitsuru Tanimura

Robert L. Bowden, D.M. Kaplan

As an illustration of a quasiclassical spin formalism developed in a recent paper a new method for solving the one-dimensional Ising model is presented. The method used is an extension to spin systems of the Wigner method familiar in computations involving position and momentum. The partition function, pair correlation function and the zero-field susceptibility for the one-dimensional Ising model with arbitrary spin are shown to be expressed in terms of the eigenfunctions and eigenvalues of a certain integral equation whose kernel approaches the classical kernel as the spin approaches infinity.

Mituru Tanimura, Norikiyo Ury

For the one-dimensional Ising model in which the interactions are usually confined in the limited range, an extension of the concept of exchange interaction has been made. In the case of unusual Ising models with arbitrary interactions between arbitrary spins some dual formula of the partition function is obtained in a closed form. In the present paper, part I, the derivation of its general formula and the application to some simple examples are shown.

Hadey K. Mohamad

J. Szṅajd

Abstract A method of the reduction of the generalized arbitrary spin two‐dimensional Ising model to the spin‐half Ising model is presented. The method is demonstrated in detail by calculating the effective interaction constants to the third order in a cumulant expansion for the triangular spin‐one Ising model (the Blume‐Emery‐Griffiths model).