Ising model with spins S=1/2 and 1 on directed and undirected Erdös–Rényi random graphs

F.W.S. Lima and M.A. Sumour

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 4, 948-953

Abstract: Using Monte Carlo simulations, we study the Ising model with spin S=1/2 and 1 on directed and undirected Erdös–Rényi (ER) random graphs, with z neighbors for each spin. In the case with spin S=1/2, the undirected and directed ER graphs present a spontaneous magnetization in the universality class of mean field theory, where in both directed and undirected ER graphs the model presents a spontaneous magnetization at p=z/N(z=2,3,…,N), but no spontaneous magnetization at p=1/N which is the percolation threshold. For both directed and undirected ER graphs with spin S=1, we find a first-order phase transition for z=4 and 9 neighbors.

Keywords: Monte Carlo simulation; Spins; Networks; Ising; Graphs (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:4:p:948-953

DOI: 10.1016/j.physa.2011.11.026

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