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

Source: [Boundary fluctuation dynamics of a phase-separated domain in planar geometry](<https://www.sota2.com/research/paper/68fa41f91e209131ce8feb38>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:54:32.870Z

Authors: Nicolas Destainville, Nelly Coulonges

Published: 2022-03-03T19:18:58.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2203.01970>)

[PDF](<https://arxiv.org/pdf/2203.01970.pdf>)