Finite-Size Effects in Dynamics: Critical vs Coarsening Phenomena

TL;DR

This paper investigates finite-size effects in systems with diverging lengthscales, confirming non-trivial singularities in critical phenomena and domain coarsening, and demonstrating the universality of finite-size effects in domain growth.

Contribution

It provides a comprehensive analysis of finite-size effects using simulations and scaling theory, revealing their universality and differences between critical and coarsening phenomena.

Findings

Finite-size effects in domain growth are weak and universal.

Finite-size effects in critical phenomena differ between statics and dynamics.

Simulations confirm analytical predictions of singularities in dynamic phenomena.

Abstract

Finite-size effects in systems with diverging characteristic lengthscale have been addressed via state-of-the-art Monte Carlo and molecular dynamics simulations of various models exhibiting solid-solid, liquid-liquid and vapor-liquid transitions. Our simulations, combined with the appropriate application of finite-size scaling theory, confirm various non-trivial singularities in equilibrium dynamic critical phenomena and non-equilibrium domain coarsening phenomena, as predicted by analytical theories. We convincingly demonstrate that the finite-size effects in the domain growth problems, with conserved order parameter dynamics, is weak and universal, irrespective of the transport mechanism. This result is strikingly different from the corresponding effects in critical dynamics. In critical phenomena, difference in finite-size effects between statics and dynamics is also discussed.