Abstract: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.
From: Jianping Jiang [view email]
[v1]
Mon, 8 Dec 2025 13:41:58 UTC (52 KB)
[v2]
Thu, 20 Aug 2026 12:35:15 UTC (49 KB)
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