Spin glass behavior of the antiferromagnetic Ising model on a scale-free network

TL;DR

This paper investigates the spin glass behavior of antiferromagnetic Ising spins on a scale-free network, identifying a phase transition and estimating critical parameters using Monte Carlo simulations.

Contribution

It introduces a Monte Carlo study of antiferromagnetic Ising spins on scale-free networks, revealing a spin glass transition and estimating critical exponents.

Findings

Transition between paramagnetic and spin glass phases at T ~ 4.0

Estimated critical exponent ν ~ 1.10

Identified phase transition using Binder parameter scaling

Abstract

Antiferromagnetic Ising spins on the scale-free Barabasi-Albert network are studied via the Monte Carlo method. Using the replica exchange algorithm, we calculate the temperature dependence of various physical quantities of interest including the overlap and the Binder parameters. We observe a transition between a paramagnetic phase and a spin glass phase and estimate the critical temperature for the phase transition to be $T \sim 4.0(1)$ in units of $J/k_B$, where $J$ is the coupling strength between spins and $k_B$ is the Boltzmann constant. Using the scaling behaviour of the Binder parameter, we estimate the scaling exponent to be $\nu \sim 1.10(2)$.