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 (Print)9789814304634, 981430462X, 9789814304627
DOIs
StatePublished - Jan 1 2010

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Glauber Dynamics
Mixing Time
Spin Systems
Critical Temperature
critical temperature
Convergence to Equilibrium
Heat Bath
Spectral Gap
Surface area
Ising Model
Continuous Time
Logarithmic
Ising model
Polynomial
baths
polynomials
cut-off
heat
geometry
Model

ASJC Scopus subject areas

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

Cite this

Lubetzky, E. (2010). Glauber dynamics for spin systems at high and critical temperatures. In XVIth International Congress on Mathematical Physics (pp. 464-469). World Scientific Publishing Co.. https://doi.org/10.1142/9789814304634_0036

Glauber dynamics for spin systems at high and critical temperatures. / Lubetzky, Eyal.

XVIth International Congress on Mathematical Physics. World Scientific Publishing Co., 2010. p. 464-469.

Research output: Chapter in Book/Report/Conference proceedingChapter

Lubetzky, E 2010, Glauber dynamics for spin systems at high and critical temperatures. in XVIth International Congress on Mathematical Physics. World Scientific Publishing Co., pp. 464-469. https://doi.org/10.1142/9789814304634_0036
Lubetzky E. Glauber dynamics for spin systems at high and critical temperatures. In XVIth International Congress on Mathematical Physics. World Scientific Publishing Co. 2010. p. 464-469 https://doi.org/10.1142/9789814304634_0036
Lubetzky, Eyal. / Glauber dynamics for spin systems at high and critical temperatures. XVIth International Congress on Mathematical Physics. World Scientific Publishing Co., 2010. pp. 464-469
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