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Phase transitions in the Ising model on random graphs
Preprint

Phase transitions in the Ising model on random graphs

Artem Alexandrov and Georgi S Medvedev
ArXiv.org
13 Nov 2025
url
https://arxiv.org/pdf/2511.10838View
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Abstract

Mathematics - Mathematical Physics Physics - Mathematical Physics Physics - Pattern Formation and Solitons Physics - Statistical Mechanics
We study phase transitions in the Ising model on random graphs using graph limits. This framework extends mean-field theory to heterogeneous nonlocal interactions. We show that the critical temperatures are determined by the eigenvalues of the kernel operator associated with the graph limit. Bifurcation diagrams for Erdos-Renyi, small-world, and power-law graphs illustrate the theory. In the small-world case, we identify metastable behavior in both ferromagnetic and antiferromagnetic regimes.

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