Application of large deviation theory to the mean-field phi^4-model

TL;DR

This paper applies large deviation theory to analyze the mean-field phi^4-model, deriving the microcanonical entropy and identifying a continuous phase transition with an analytical critical energy expression.

Contribution

It introduces a large deviation approach to compute microcanonical entropy and phase transition properties in the mean-field phi^4-model, providing analytical results.

Findings

Identifies a continuous phase transition in the model.

Derives an explicit formula for the critical energy v_c(J).

Shows consistency with canonical ensemble results.

Abstract

A large deviation technique is used to calculate the microcanonical entropy function s(v,m) of the mean-field phi^4-model as a function of the potential energy v and the magnetization m. As in the canonical ensemble, a continuous phase transition is found. An analytical expression is obtained for the critical energy v_c(J) as a function of the coupling parameter J.