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Bibliographic Details
Main Authors: Jiang, Jianping, Lang, Sike
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.21147
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Table of Contents:
  • Let $\mathbb{T}$ be the two-dimensional triangular lattice, and $\mathbb{Z}$ the one-dimensional integer lattice. Let $\mathbb{T}\times \mathbb{Z}$ 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 $β\in[0,β_c)$, there exists $h_c(β)>0$ such that both a unique infinite $+$cluster and a unique infinite $-$cluster coexist whenever $|h|<h_c(β)$. The same coexistence result also holds for the three-dimensional triangular lattice.