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
DOI
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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