A coupled order parameter system on a scale-free network

TL;DR

This paper investigates a coupled two-parameter system on scale-free networks, revealing unique ordering behaviors, critical properties, and divergence in susceptibility linked to Goldstone modes, combining phenomenological and microscopic approaches.

Contribution

It introduces a coupled order parameter model on scale-free networks and analyzes its critical behavior using Landau theory and a spin Hamiltonian with mean field approximation.

Findings

System exhibits two types of ordering: one order parameter zero or both non-zero with same value.

Critical exponents match single order parameter models, but amplitude ratios and susceptibilities differ.

Transverse susceptibility diverges below T_c due to Goldstone modes.

Abstract

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are non-zero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale free network there are notable differences for the amplitude ratios and susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T<T_c, when O(n) symmetry is present. This behavior is related to the appearance of Goldstone modes.