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arXiv · 2608.19605

Exact partition function of arithmetic Ising model

Anu Dhochak·Ken Kikuchi·Shrinit Singh
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Abstract

We present a compact formula for the exact partition function of the $d$-dimensional arithmetic Ising model (AIM). For a $2\times2$ system, we express it analytically using the $q$-Hurwitz-Lerch zeta function and derive explicit forms for the free energy and entropy. Additionally, we find that the entropy increases at high temperatures, supporting the presence of entropic order.

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Anu Dhochak, Ken Kikuchi, Shrinit Singh. 2026-08-20. Exact partition function of arithmetic Ising model. https://arxiv.org/abs/2608.19605

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