Percolation of both signs in a triangular-type 3D Ising model above T_c

2025/03/27 by Jianping Jiang, Jiang, Jianping, Lang, Sike
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2503.21147

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

Let \mathbbT be the two-dimensional triangular lattice, and ℤ the one-dimensional integer lattice. Let \mathbbT× ℤ denote the Cartesian product graph. Consider the Ising model defined on this graph with inverse temperature β and external field h, and let β_c be the critical inverse temperature when h=0. We prove that for each β∈[0,β_c), there exists h_c(β)>0 such that both a unique infinite +cluster and a unique infinite -cluster coexist whenever |h|

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