Low-temperature asymptotics of free energy of 3D Ising model in an external magnetic field

TL;DR

This paper develops a new method combining transfer-matrix and generalized Jordan-Wigner transformations to analyze the low-temperature behavior of the 3D Ising model's free energy in an external magnetic field, valid over a wide parameter range.

Contribution

It introduces a novel approach for calculating low-temperature asymptotics of the 3D Ising model's free energy in external magnetic fields, extending the analytical tools available.

Findings

Valid in a wide temperature and magnetic field range.

Applicable when [1 - tanh(h/2)] is small.

Utilizes transfer-matrix and generalized Jordan-Wigner methods.

Abstract

The paper presents new method for calculating the low-temperature asymptotics of free energy of the 3D Ising model in external magnetic field $(H\neq 0)$. The results obtained are valid in the wide range of temperature and magnetic field values fulfilling the condition: $[1-\tanh(h/2)]\sim\epsilon,$ for $\epsilon\ll 1$, where $h=\beta H$, $\beta$ - the inverse temperature and $H$ - external magnetic field. For this purpose the method of transfer-matrix, and generalized Jordan-Wigner transformations, in the form introduced by the author in $\cite{mkoch95}$, are applied.