A simple proof of exponential decay for the near-critical planar Ising model

2025/12/08 by Jiang, Jianping, Klausen, Frederik Ravn
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.07554

Abstract

For the Ising model defined on aℤ² at critical temperature with external field a^15/8h, 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 aℤ² with diameter of order 1, together with two external edges that connect the path's endpoints to the ghost.

Citations

• A General Coupling for Ising Models and Beyond
• The Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model
• The Gaussian process for particle masses in the near-critical Ising model
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• Random currents expansion of the Ising model
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• Random even graphs

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