Boundary fluctuation dynamics of a phase-separated domain in planar geometry

TL;DR

This paper analytically derives the relaxation times of boundary fluctuations in phase-separated domains near criticality, supported by simulations, with implications for experimental and simulation time-scale measurements.

Contribution

It provides a theoretical framework for relaxation times of domain boundaries in the planar Ising model, including non-universal prefactors, bridging theory and numerical simulations.

Findings

Relaxation time scales as the cube of wavelength for conserved order parameters.

Analytical expressions relate relaxation times to microscopic parameters.

Numerical simulations confirm theoretical predictions and determine prefactors.

Abstract

Using theories of phase ordering kinetics and of renormalization group, we derive analytically the relaxation times of the long wave-length fluctuations of a phase-separated domain boundary in the vicinity of (and below) the critical temperature, in the planar Ising universality class. For a conserved order parameter, the relaxation time grows like $\Lambda^3$ at wave-length $\Lambda$ and can be expressed in terms of parameters relevant at the microscopic scale: lattice spacing, bulk diffusion coefficient of the minority phase, and temperature. These results are supported by numerical simulations of 2D Ising models, enabling in addition to calculate the non-universal numerical prefactor. We discuss the applications of these findings to the determination of the real time-scale associated with elementary Monte Carlo moves from the measurement of long wave-length relaxation times on experimental systems or Molecular Dynamics simulations.