Superradiant phase transition in complex networks

TL;DR

This paper investigates the superradiant phase transition in the Dicke-Ising model on complex networks, revealing how network structure influences critical temperatures and phase behavior, including quantum phase transitions at zero temperature.

Contribution

It introduces a generalized model for complex networks, analyzing superradiant and magnetic phase transitions with novel features due to finite size and network topology effects.

Findings

Critical temperature increases with network size and degree exponent.

Spontaneous magnetization occurs in the quantum transverse field.

Conditions for quantum phase transition at zero temperature are established.

Abstract

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