Finite-Size Effects on Critical Diffusion and Relaxation Towards Metastable Equilibrium

TL;DR

This paper analytically investigates how finite-size effects influence critical diffusion and relaxation dynamics in 3D Ising-like systems, providing universal ratios and scaling functions for testing via simulations.

Contribution

It offers the first analytic analysis of finite-size effects on critical diffusion and relaxation in coupled order parameter systems, with new universal amplitude ratios and scaling functions.

Findings

Predicted two new universal dynamic amplitude ratios at T_c.

Derived quantitative finite-size scaling functions for critical dynamics.

Provided testable predictions for Monte-Carlo simulations.

Abstract

We present the first analytic study of finite-size effects on critical diffusion above and below T_c of three-dimensional Ising-like systems whose order parameter is coupled to a conserved density. We also calculate the finite-size relaxation time that governs the critical order-parameter relaxation towards a metastable equilibrium state below T_c. Two new universal dynamic amplitude ratios at T_c are predicted and quantitative predictions of dynamic finite-size scaling functions are given that can be tested by Monte-Carlo simulations.