Statistical Mechanics of Kinks in (1+1)-Dimensions

TL;DR

This paper studies the thermal behavior of kinks in a 1+1 dimensional classical field theory, combining large-scale simulations with theoretical models to understand their distribution, density, and correlations across temperature regimes.

Contribution

It introduces a combined simulation and analytical approach, including a double Gaussian approximation, to analyze kink properties beyond the dilute gas regime in 1+1D field theory.

Findings

Validates dilute gas approximation below a certain temperature

Extends analysis to higher temperatures using double Gaussian approximation

Accurately predicts the breakdown temperature of the kink description

Abstract

We investigate the thermal equilibrium properties of kinks in a classical $\phi^4$ field theory in $1+1$ dimensions. The distribution function, kink density, and correlation function are determined from large scale simulations. A dilute gas description of kinks is shown to be valid below a characteristic temperature. A double Gaussian approximation to evaluate the eigenvalues of the transfer operator enables us to extend the theoretical analysis to higher temperatures where the dilute gas approximation fails. This approach accurately predicts the temperature at which the kink description breaks down.