A simple proof of exponential decay for the near-critical planar Ising model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908698166689792 |
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| author | Jiang, Jianping Klausen, Frederik Ravn |
| author_facet | Jiang, Jianping Klausen, Frederik Ravn |
| contents | For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high temperature expansion, random-cluster and random current representations. A new input in the proof is that, in the near-critical sourceless single current measure, there are many loops formed by a path on $a\mathbb{Z}^2$ with diameter of order $1$, together with two external edges that connect the path's endpoints to the ghost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A simple proof of exponential decay for the near-critical planar Ising model Jiang, Jianping Klausen, Frederik Ravn Probability Mathematical Physics For the Ising model defined on $a\mathbb{Z}^2$ at critical temperature with external field $a^{15/8}h$, we give a simple and elementary proof that its truncated two-point function decays exponentially. The proof combines the high temperature expansion, random-cluster and random current representations. A new input in the proof is that, in the near-critical sourceless single current measure, there are many loops formed by a path on $a\mathbb{Z}^2$ with diameter of order $1$, together with two external edges that connect the path's endpoints to the ghost. |
| title | A simple proof of exponential decay for the near-critical planar Ising model |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2512.07554 |