Improved harmonic approximation and the 2D Ising model at $T\neq T_{c}$ and $h\neq0$

TL;DR

This paper introduces a new method for self-consistent harmonic approximation, validated on the sine-Gordon model, and applied to analyze the 2D Ising model away from criticality with an external magnetic field.

Contribution

It presents a novel technique to determine the self-consistent harmonic parameter and applies it to the 2D Ising model in a non-critical regime with magnetic field.

Findings

Derived an expression linking correlation length, temperature deviation, and magnetic field.

Validated the method using the sine-Gordon model.

Provided insights into the scaling behavior of the 2D Ising model away from criticality.

Abstract

We propose a new method to determine the unknown parameter associated to a self-consistent harmonic approximation. We check the validity of our technique in the context of the sine-Gordon model. As a non trivial application we consider the scaling regime of the 2D Ising model away from the critical point and in the presence of a magnetic field $h$. We derive an expression that relates the approximate correlation length $\xi$, $T-T_c$ and $h$.