Layered systems at the mean field critical temperature

Abstract

We consider the Ising model on $\mathbb{Z}\times \mathbb{Z}$ where on each horizontal line $\{(x,i),x\in \mathbb{Z}\}$, the interaction is given by a ferromagnetic Kac potential with coupling strength $J_{\gamma }(x,y)\sim \gamma J(\gamma (x-y))$ at the mean field critical temperature. We then add a nearest neighbor ferromagnetic vertical interaction of strength $\epsilon$ and prove that for every $\epsilon >0$ the systems exhibits phase transition provided $\gamma >0$ is small enough.

35 pages

References in corpus (2)

• The Phase Diagram of the Quantum Curie-Weiss Model
• Phase transitions in layered systems

Cited by in corpus (5)

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• Dimensional Crossover in Anisotropic Percolation on $Z^{d+s}$
• A note on the dimensional crossover critical exponent
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