Dynamic critical phenomena in disordered systems with finite geometry

TL;DR

This paper investigates the critical dynamics of finite disordered systems near the upper critical dimension, deriving finite-size scaling expressions for relaxation time using renormalization group methods.

Contribution

It provides a first-order epsilon expansion for relaxation time in finite disordered systems, incorporating finite-size effects in the critical dynamics.

Findings

Derived finite-size scaling expressions for relaxation time.

Analyzed finite-size effects on the Onsager kinetic coefficient.

Compared results with existing literature.

Abstract

We study the critical dynamics of hyper-cubic finite size system in the presence of quenched short-range correlated disorder. By using the random $T_c$ model A for the critical dynamics and the renormalization group method in the vicinity of the upper critical dimension $d=4$, we derive in first order of $\epsilon$ the expression for the relaxation time. Its finite-size scaling behavior is discussed both analytically and numerically in details. This was made possible by analyzing carefully the finite--size effects on the Onsager kinetic coefficient. The obtained results are compared to those reported in the literature.