A Two-populations Ising model on diluted Random Graphs

TL;DR

This paper investigates a two-population Ising model on diluted Erdős-Rényi graphs, revealing a phase transition influenced by interaction strength and population heterogeneity, with critical exponents aligning with the Curie-Weiss model.

Contribution

It introduces a detailed analysis of phase transitions in a two-population Ising model on diluted random graphs, highlighting the dependence of critical points on graph dilution and population ratios.

Findings

Existence of a phase transition at a critical inter-group coupling

Critical coupling depends algebraically on graph dilution and population width

Critical exponents match those of the Curie-Weiss model

Abstract

We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the existence of a phase transition at a value of the inter-groups interaction coupling $J_{12}^C$ which depends algebraically on the dilution of the graph and on the relative width of the two populations, as explained by means of scaling arguments. We also measure the critical exponents, which are consistent with those of the Curie-Weiss model, hence suggesting a wide robustness of the universality class.