Glauber dynamics of 2D Kac–Blume–Capel model and their stochastic PDE limits

Hao Shen, Hendrik Weber

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study the Glauber dynamics of a two dimensional Blume–Capel model (or dilute Ising model) with Kac potential parametrized by (β,θ) – the “inverse temperature” and the “chemical potential”. We prove that the locally averaged spin field rescales to the solution of the dynamical Φ4 equation near a curve in the (β,θ) plane and to the solution of the dynamical Φ6 equation near one point on this curve. Our proof relies on a discrete implementation of Da Prato–Debussche method [13] as in [33] but an additional coupling argument is needed to show convergence of the linearized dynamics.

Original languageEnglish
Pages (from-to)1321-1367
JournalJournal of Functional Analysis
Volume275
Issue number6
Early online date20 Jun 2018
DOIs
Publication statusPublished - 15 Sep 2018

Keywords

  • Blume–Capel
  • Glauber dynamics
  • Stochastic PDE

ASJC Scopus subject areas

  • Analysis

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