First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory

Details First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory

2010-01-08

arxiv.org/abs/1001.1342v2

Phys. Rev. E 82, 011141 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 12 figures, 1 table

Scientific paper

10.1103/PhysRevE.82.011141

We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of multicritical points with first- or second-order phase transitions. In particular, for second-order phase transitions, independent of the dimension d_0 of the underlying lattice, the exact predictions of the theory in the paramagnetic regions, such as the location of critical surfaces and correlation functions, are verified. Quite interestingly, we verify that the Edwards-Anderson model with d_0=2 is not thermodynamically stable under graph noise.

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