Antiferromagnetic Ising model in scale-free networks

TL;DR

This paper investigates how the antiferromagnetic Ising model behaves on uncorrelated scale-free networks, revealing a spin-glass phase at low temperatures influenced by network degree distribution.

Contribution

It provides the first Monte Carlo simulation analysis of the antiferromagnetic Ising model on scale-free networks, exploring the transition temperature dependence on network parameters.

Findings

Transition temperature T_c increases as gamma decreases.

Presence of high-degree nodes enhances frustration and spin-glass behavior.

Spin-glass phase emerges at low temperatures due to network disorder.

Abstract

The antiferromagnetic Ising model in uncorrelated scale-free networks has been studied by means of Monte Carlo simulations. These networks are characterized by a connectivity (or degree) distribution P(k) ~ k^(- gamma). The disorder present in these complex networks frustrates the antiferromagnetic spin ordering, giving rise to a spin-glass (SG) phase at low temperature. The paramagnetic-SG transition temperature T_c has been studied as a function of the parameter gamma and the minimum degree present in the networks. T_c is found to increase when the exponent gamma is reduced, in line with a larger frustration caused by the presence of nodes with higher degree.