Anisotropic Ising model in d+s dimensions

2024/04/10 by Estevãoo F. Borel, Borel, Estevão F., Aldo Procacci +5
Mathematics · Physics and Astronomy · #82B20 #82B26 #Complex Network Analysis Techniques #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2404.07079

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this note, we consider the asymmetric nearest neighbor ferromagnetic Ising model on the (d+s)-dimensional unit cubic lattice \Z^d+s, at inverse temperature β=1 and with coupling constants J_s>0 and J_d>0 for edges of \Z^s and \Z^d, respectively. We obtain a lower bound for the critical curve in the phase diagram of (J_s,J_d). In particular, as J_d approaches its critical value from below, our result is directly related to the so-called dimensional crossover phenomenon.

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