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

Abstract

Antiferromagnetic Ising spins on the scale-free Barab\'asi-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 $T\ensuremath{\sim}4.0(1)$ in units of $J∕{k}_{B}$, where $J$ is the coupling strength between spins and ${k}_{B}$ is the Boltzmann constant. Using the scaling behavior of the Binder parameter, we estimate the scaling exponent to be $\ensuremath{\nu}\ensuremath{\sim}1.10(2)$.

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