Lenz-Ising-Onsager problem in an external field as a soluble problem of many fermions

TL;DR

This paper introduces a novel method for solving the 2D and 3D Ising models in external magnetic fields, extending Onsager's solution and analyzing low-temperature free energy asymptotics.

Contribution

It develops a new approach to solve the Ising models in external fields, providing a generalized formalism and asymptotic analysis of free energy.

Findings

New method reproduces Onsager solution in zero field

Asymptotic forms of low-temperature free energy derived

Analysis of free energy as magnetic field approaches zero

Abstract

In this paper a new approach to solving the 2D and 3D Ising models in external magnetic field $H\neq0$ is developed. The general formalism for the approach to the problem is presented on the example of the 2D Ising model in the external magnetic field. The paper presents a new method obtaining the Onsager solution and computations of asymptotic forms of low-temperature free energy for the 2D Ising model in the external magnetic field $(H)$. The free energy in the limiting case of the magnetic field tending to zero $(H\to 0, N,M\to\infty)$ at arbitrary temperature is also considered $(T\neq 0)$.