WIAS Preprint No. 894, (2003)

Coarse-graining techniques for (random) Kac models



Authors

  • Bovier, Anton
  • Külske, Christof

2010 Mathematics Subject Classification

  • 82B44 82B20 82B28

2008 Physics and Astronomy Classification Scheme

  • 05.10.Cc

Keywords

  • Kac models, phase transitions, random field model, renormalization group, coarse-graining

Abstract

We review our recent results on the low temperature behavior of Kac models. We discuss translation-invariant models and the Kac version of the random field model. For the latter we outline, how various coarse-graining techniques can be used to prove ferromagnetic ordering in dimensions $dgeq 3$, small randomness, and low temperatures, uniformly in the range of the interaction.

Appeared in

  • Interacting Stochastic Systems, J. Deuschel, A. Greven (eds.), Springer, Berlin--Heidelberg, 2005, pp. 11--28

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