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arXiv · 2307.10742

High-temperature cluster expansion for classical and quantum spin lattice systems with multi-body interactions

Nguyen Tong Xuan·Roberto Fernandez
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Abstract

We develop a novel cluster expansion for finite-spin lattice systems subject to multi-body quantum -- and, in particular, classical -- interactions. Our approach is based on the use of ``decoupling parameters", advocated by Park [34], which relates partition functions with successive additional interaction terms. Our treatment, however, leads to an explicit expansion in a $\beta$-dependent effective fugacity that permits an explicit evaluation of free energy and correlation functions at small $\beta$. To determine its convergence region we adopt a relatively recent cluster summation scheme that replaces the traditional use of Kikwood-Salzburg-like integral equations by more precise sums in terms of particular tree-diagrams [2]. As an application we show that our lower bound of the radius of $\beta$-analyticity is larger than Park's for quantum systems two-body interactions.

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Nguyen Tong Xuan, Roberto Fernandez. 2023-07-20. High-temperature cluster expansion for classical and quantum spin lattice systems with multi-body interactions. https://arxiv.org/abs/2307.10742

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