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arXiv · 2508.15666

Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models

Lucas Affonso·Rodrigo Bissacot·João Maia·João F. Rodrigues·Kelvyn Welsch
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Abstract

We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^\alpha$, $J>0$, and $\alpha>d$. As an application of the convergence of the cluster expansion at low temperatures, we study the decay of the truncated two-point correlation functions, showing that the decay is algebraic with coefficient $\alpha$.

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Lucas Affonso, Rodrigo Bissacot, João Maia, João F. Rodrigues, Kelvyn Welsch. 2025-08-21. Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models. https://arxiv.org/abs/2508.15666

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