On the two- and three-dimensional Lenz-Ising-Onsager problem in presence of magnetic field

TL;DR

This paper introduces a new approach to solving the Ising-Onsager problem with magnetic fields, deriving free energy expressions for 2D and 3D models using multidimensional integrals, and explores their calculation and critical behavior.

Contribution

It presents a novel method for deriving free energy expressions for the Ising model in magnetic fields using multidimensional integrals, applicable to 2D and 3D cases.

Findings

Derived free energy expressions as multidimensional integrals

Analyzed the potential for calculating these integrals

Investigated critical indices based on the new representations

Abstract

In this paper a new approach to solving the Ising-Onsager problem in external magnetic field is investigated. The expression for free energy on one Ising spin in external field both for the twodimensional and threedimensional Ising model with interaction of the nearest neighbors are derived. The representations of free energy being expressed by multidimensional integrals of Gauss type with the appropriate dimensionality are shown. Possibility of calculating the integrals and the critical indices on the base of the derived representations for free energy is investigated.