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Generalized mean-field theory for Ising spins in small world networks
E Z Meilikhov1, R M Farzetdinova
1RRC Kurchatov Institute, 123182 Moscow, Russia.
Abstract:
A generalization of mean-field theory for random systems is described. The results of that analytic model could be reconciled with the results of numerical calculations of the Curie temperature for a system of Ising spins in small world (SW) networks by introducing the effective interaction energy associated with long-range links which exceeds the real energy of spin interaction. Such a model describes qualitatively well the increasing Curie temperature T(C) with the growth of the long-range links fraction p in the two-dimensional SW system with fixed coordination number. On the basis of simple physical considerations, concentration dependences T(C)(p) are found for SW systems of different dimensions.
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