Gaussian fluctuations for the classical XY model

Research output: Contribution to journalArticlepeer-review

Abstract

We study the classical XY model in bounded domains of Zd with Dirichlet boundary conditions. We prove that when the temperature goes to zero faster than a certain rate as the lattice spacing goes to zero, the fluctuation field converges to a Gaussian white noise. This and related results also apply to a large class of gradient field models.

Original languageEnglish (US)
Pages (from-to)1759-1777
Number of pages19
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume54
Issue number4
DOIs
StatePublished - Nov 2018

Keywords

  • Central limit theorem
  • Gaussian free field
  • Gradient field models
  • Random walk representation
  • Spin-wave approximation
  • XY model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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