A set of exactly solvable Ising models with half-odd-integer spin

TL;DR

This paper introduces a family of exactly solvable Ising models with half-odd-integer spins on a square lattice, utilizing mappings to eight-vertex models satisfying free fermion conditions, expanding solvable spin configurations.

Contribution

It provides a new set of exactly solvable Ising models with half-odd-integer spins and quartic interactions, generalizing previous models and revealing their connection to free fermion solutions.

Findings

Exact solutions satisfy the free fermion condition of the eight vertex model.

Number of solutions for spin-S is S+1/2.

Mapping to spin-1/2 or spin-S lattices is possible.

Abstract

We present a set of exactly solvable Ising models, with half-odd-integer spin-S on a square-type lattice including a quartic interaction term in the Hamiltonian. The particular properties of the mixed lattice, associated with mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction, allow us to map this system either onto a purely spin-1/2 lattice or onto a purely spin-S lattice. By imposing the condition that the mixed half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a set of exact solutions that satisfy the {\it free fermion} condition of the eight vertex model. The number of solutions for a general half-odd-integer spin-S is given by $S+1/2$. Therefore we conclude that this transformation is equivalent to a simple spin transformation which is independent of the coordination number.