Global Persistence Exponent in Critical Dynamics: Finite Size induced Crossover

TL;DR

This paper investigates how finite system size influences the persistence behavior of a global order parameter at criticality, revealing a crossover characterized by a non-universal exponent dependent on system size and dynamic length scales.

Contribution

It extends the global order parameter concept to confined critical systems and uncovers a finite size induced crossover in persistence behavior.

Findings

Identification of a crossover in persistence behavior due to finite size effects.

Discovery of a non-universal exponent depending on system size and dynamic length.

Demonstration of finite size effects on critical dynamics in confined geometries.

Abstract

We extend the definition of a global order parameter to the case of a critical system confined between two infinite parallel plates separated by a finite distance $L$. For a quench to the critical point we study the persistence property of the global order parameter and show that there is a crossover behaviour characterized by a non universal exponent which depends on the ratio of the system size to a dynamic length scale.