Preprint
Phase transitions in the Ising model on random graphs
ArXiv.org
13 Nov 2025
Abstract
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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Details
- Title
- Phase transitions in the Ising model on random graphs
- Creators
- Artem AlexandrovGeorgi S Medvedev
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022133633804721