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 Dicke and Ising models annealed complex networks presuming spin-spin interaction. The model accounts interaction between spin (two-level) system external classical (magnetic) quantized (transverse) fields. We examine regular, random, scale-free network structures characterized by delta-function, random (Poisson), power-law exponent degree distributions, respectively. To describe paramagnetic (PM) - ferromagnetic (FM) (SR) transitions introduce two order parameters: total weighted z-component normalized transverse field amplitude, correspond to spontaneous magnetization in z x directions, Due interplay finite size effects first elucidate novel features of SR state presence PM-FM transition. reveal that critical temperature grows monotonically from some certain value corresponds number nodes. For find rises with increase accompanied both establishing quantum vanishing collective component direction. addition, establish conditions parameters obtain when approaches zero. fundamental features, involve values parameters, are discussed occurrence superradiance limit.