Phase transitions in the Ising model on random graphs
Mathematical Physics
2025-12-01 v2 Statistical Mechanics
math.MP
Pattern Formation and Solitons
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.
Cite
@article{arxiv.2511.10838,
title = {Phase transitions in the Ising model on random graphs},
author = {Artem Alexandrov and Georgi S. Medvedev},
journal= {arXiv preprint arXiv:2511.10838},
year = {2025}
}