Exact formula for the magnetization of the Ising model

Masuo Suzuki

Keh-Ying Lin

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.

Alessandro Pelizzola

An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact. By taking the limit where the width of the strip approaches infinity and the interactions have well-defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst-van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort.

B G S Doman

Ken‐Yu Lin

A formula for the spontaneous magnetization of the Ising model on a checkerboard lattice with crossing interactions is proposed. Our conjecture agrees with the exact low-temperature series expansion up to the 18th order.