Glauber dynamics for spin systems at high and critical temperatures

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The spectral gap of the continuous-time heat-bath Glauber dynamics for the Ising model on the lattice is believed to exhibit the following behavior. For some critical-inverse temperature βc, the mixing-time of the dynamics is logarithmic in the surface-area for β “ βc, polynomial for β = βc and exponential for β > βc. Furthermore, for β “ βc the mixing time is sharply concentrated and the dynamics exhibits the cutoff phenomenon, an abrupt convergence to equilibrium. We survey the recent progress in confirming this picture for various underlying geometries and spin system models.

Original languageEnglish (US)
Title of host publicationXVIth International Congress on Mathematical Physics
PublisherWorld Scientific Publishing Co.
Pages464-469
Number of pages6
ISBN (Electronic)9789814304634
ISBN (Print)981430462X, 9789814304627
DOIs
StatePublished - Jan 1 2010

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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