Highly anisotropic scaling limits
| Autor: | Marzio Cassandro, Matteo Colangeli, Errico Presutti |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Physics
Condensed matter physics Spins Probability (math.PR) FOS: Physical sciences Statistical and Nonlinear Physics 02 engineering and technology Mathematical Physics (math-ph) 021001 nanoscience & nanotechnology Critical value 01 natural sciences Ferromagnetism Mean field theory 0103 physical sciences Mathematical Physics FOS: Mathematics Limit (mathematics) 010306 general physics 0210 nano-technology Anisotropy Spontaneous magnetization Scaling Mathematics - Probability |
| DOI: | 10.48550/arxiv.1507.05770 |
| Popis: | We consider a highly anisotropic \(d=2\) Ising spin model whose precise definition can be found at the beginning of Sect. 2. In this model the spins on a same horizontal line (layer) interact via a \(d=1\) Kac potential while the vertical interaction is between nearest neighbors, both interactions being ferromagnetic. The temperature is set equal to 1 which is the mean field critical value, so that the mean field limit for the Kac potential alone does not have a spontaneous magnetization. We compute the phase diagram of the full system in the Lebowitz–Penrose limit showing that due to the vertical interaction it has a spontaneous magnetization. The result is not covered by the Lebowitz–Penrose theory because our Kac potential has support on regions of positive codimension. |
| Databáze: | OpenAIRE |
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