Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model

T. Funaki, H. Spohn

Research output: Contribution to journalArticle

89 Citations (Scopus)

Abstract

We consider the scalar field φt with a reversible stochastic dynamics which is defined by the standard Dirichlet form relative to the Gibbs measure with formal energy ∫ ddxV(▽φ(x)). The potential V is even and strictly convex. We prove that under a suitable large scale limit the φt-field becomes deterministic such that locally its normal velocity is proportional to its mean curvature, except for some anisotropy effects. As an essential input we prove that for every tilt there is a unique shift invariant, ergodic Gibbs measure for the ▽φ-field.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalCommunications in Mathematical Physics
Volume185
Issue number1
DOIs
Publication statusPublished - 1997 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Fingerprint Dive into the research topics of 'Motion by mean curvature from the Ginzburg-Landau ▽ φ interface model'. Together they form a unique fingerprint.

  • Cite this