Mean-field theory of superradiant phase transition in complex networks.

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the δ function, random (Poisson), and power-law exponent [p(k)∝k^{-γ}] degree distributions, respectively.