Ansatz for the Two-Dimensional Ising Model in an External Magnetic Field

TL;DR

This paper introduces an ansatz that makes the two-dimensional Ising model with an external magnetic field exactly solvable, revealing how magnetic field affects singularities in magnetization and heat capacity.

Contribution

The study presents a new ansatz that simplifies the 2D Ising model with magnetic field, providing exact solutions and insights into phase transition singularities.

Findings

Magnetization singularity disappears with magnetic field

Heat capacity singularity persists despite magnetic field

Negative heat capacity observed for h > 0

Abstract

An ansatz applied to the two-dimensional Ising model in an external magnetic field h gives rise to an exactly soluble model. The singularity in the magnetization found by Onsager does not survive the presence of the external magnetic field as found earlier by Lee and Yang in 1952. However, the singularity in the heat capacity remains even in the presence of the magnetic field. A surprising result is the presence of negative heat capacity for h > 0.