Disorder solutions for the partition functions of the two-dimensional Ising-like models

TL;DR

This paper derives formulas for the partition function and free energy of generalized 2D Ising-like models with complex interactions, providing exact disordered solutions for various specific cases including models with external fields and multi-spin interactions.

Contribution

It introduces a set of exact disordered solutions for a broad class of 2D Ising-like models, expanding analytical understanding of these systems.

Findings

Derived formulas for partition functions and free energies in generalized models

Obtained disordered solutions for models with various interaction types

Extended solutions to models with external magnetic fields and multi-spin interactions

Abstract

For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the general case, 8-dimensional subset of exact disordered solutions of 10-dimensional set of the Hamiltonian's parameters. When a part of parameters are set to zero, as a consequence, the disorder solutions were got for the models with nearest, next-nearest-neighbor and the interaction of four spins in an external field and without an external field, triangular and "checkerboard-triangular" Ising models with triple interactions in an external magnetic field.