Scaling Function for the Diffusion Coefficient of a Critical Fluid in a Finite Geometry

TL;DR

This paper investigates how the diffusion coefficient of a critical fluid confined between two plates scales with system size and correlation length, revealing a logarithmic correction to the expected finite size scaling.

Contribution

The authors develop a Kawasaki-like scaling function that accurately describes the crossover from thermodynamic to critical regimes, including a logarithmic scaling violation.

Findings

Finite size scaling is modified by a logarithmic correction.

A new scaling function connects different critical regimes.

The diffusion coefficient's behavior deviates from simple inverse proportionality.

Abstract

The long wavelength diffusion coefficient of a critical fluid confined between two parallel plates separated by a distance L is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion coefficient as \xi^{-1} for \xi<<L, \xi being the correlation length, would crossover to \L^{-1} for \xi>>L. We show that this is not strictlytrue. There is a logarthmic scaling violation. We construct a Kawasaki like scaling function that connects the thermodynamic regime to the extreme critical (\xi>>L) regime.