Phase transitions in the Ising model on random graphs

Artem Alexandrov; Georgi S. Medvedev

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arXiv · 2511.10838

Phase transitions in the Ising model on random graphs

Artem Alexandrov·Georgi S. Medvedev

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Abstract

We study phase transitions in the Ising model on random graphs using graph limits. 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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Artem Alexandrov, Georgi S. Medvedev. 2025-11-26. Phase transitions in the Ising model on random graphs. https://arxiv.org/abs/2511.10838

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