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.

Highly Anisotropic Scaling Limits

CASSANDRO, Marzio;COLANGELI, MATTEO;PRESUTTI, ERRICO
2016

Abstract

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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/111711
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact