Renewal properties of the d = 1 Ising model
| Autor: | Errico Presutti, Marzio Cassandro, Immacolata Merola |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Phase transition
FOS: Physical sciences 82B05 82B20 60K05 01 natural sciences Measure (mathematics) 1D Ising model cluster expansion coarse graining Kac potential renewal process Statistical and Nonlinear Physics Mathematical Physics Magnetization 0103 physical sciences Computer Science::General Literature Renewal theory 0101 mathematics Scaling Mathematical physics Spin-½ Physics Computer Science::Information Retrieval 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Mathematical Physics (math-ph) Mean field theory Ising model 010307 mathematical physics |
| Zdroj: | Reviews in Mathematical Physics. 30:1850018 |
| ISSN: | 1793-6659 0129-055X |
| DOI: | 10.1142/s0129055x18500186 |
| Popis: | We consider the [Formula: see text] Ising model with Kac potentials at inverse temperature [Formula: see text] where the mean field predicts a phase transition with two possible equilibrium magnetizations [Formula: see text], [Formula: see text]. We show that when the Kac scaling parameter [Formula: see text] is sufficiently small, typical spin configurations are described (via a coarse graining) by an infinite sequence of successive plus and minus intervals where the empirical magnetization is “close” to [Formula: see text], and respectively, [Formula: see text]. We prove that the corresponding marginal of the unique DLR measure is a renewal process. |
| Databáze: | OpenAIRE |
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