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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.21147 |
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| _version_ | 1866908713714974720 |
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| author | Jiang, Jianping Lang, Sike |
| author_facet | Jiang, Jianping Lang, Sike |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Percolation of both signs in a triangular-type 3D Ising model above $T_c$ Jiang, Jianping Lang, Sike Probability Mathematical Physics 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. |
| title | Percolation of both signs in a triangular-type 3D Ising model above $T_c$ |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2503.21147 |