Phase transitions induced by microscopic disorder: a study based on the order parameter expansion

TL;DR

This paper introduces an approximate method based on order parameter expansion to analyze phase transitions caused by microscopic disorder, simplifying complex systems to three key equations and validating results through numerical and finite-size analyses.

Contribution

The paper presents a novel approximate approach that reduces large coupled systems to three equations, enabling efficient analysis of disorder-induced phase transitions.

Findings

The method accurately predicts phase transition behavior.

Disorder can induce or destroy macroscopic order.

Critical exponents are calculated through finite-size analysis.

Abstract

Based on the order parameter expansion, we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations: one for the global, mean field, variable and two which describe the fluctuations around this mean value. With this tool we analyze phase-transitions induced by microscopic disorder in three prototypical models of phase-transitions which have been studied previously in the presence of thermal noise. We study how macroscopic order is induced or destroyed by time independent local disorder and analyze the limits of the approximation by comparing the results with the numerical solutions of the self-consistency equation which arises from the property of self-averaging. Finally, we carry on a finite-size analysis of the numerical results and calculate the corresponding critical exponents.