Highly Anisotropic Scaling Limits

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 bein...

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Bibliographic Details
Published inJournal of statistical physics Vol. 162; no. 4; pp. 997 - 1030
Main Authors Cassandro, M., Colangeli, M., Presutti, E.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2016
Springer
Subjects
Analysis
Anisotropy
Ferromagnetism
Magnetization
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Auxiliary Magnetic Field
Spontaneous Magnetization
Lebowitz-Penrose Limit
Vertical Interaction
Positive Codimension
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Summary: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.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1437-0