A Two-populations Ising model on diluted Random Graphs

Abstract

We consider the Ising model for two interacting groups of spins embedded in an Erdös-Rényi 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.

11 pages, 4 figures

References in corpus (10)

• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• The Harris-Luck criterion for random lattices
• Phase transitions in social sciences: two-populations mean field theory
• Approximation schemes for the dynamics of diluted spin models: the Ising ferromagnet on a Bethe lattice
• Criticality in diluted ferromagnet
• Mean field dilute ferromagnet I. High temperature and zero temperature behavior
• Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
• Finite Size Effects for the Ising Model on Random Graphs with Varying Dilution
• Dilution Robustness for Mean Field Ferromagnets

Cited by in corpus (1)

• Instability and network effects in innovative markets