Antiferromagnetic Ising model in small-world networks

TL;DR

This study investigates how introducing disorder in small-world networks affects the antiferromagnetic Ising model, revealing a transition to a spin-glass phase and how the transition temperature varies with disorder.

Contribution

It provides a detailed analysis of the phase transition and disorder effects in the antiferromagnetic Ising model on small-world networks using Monte Carlo simulations.

Findings

Transition temperature decreases with increasing disorder p.

Saturation of transition temperature at approximately 1.7 J for p > 0.4.

Energy increases linearly with p at low temperature and small p.

Abstract

The antiferromagnetic Ising model in small-world networks generated from two-dimensional regular lattices has been studied. The disorder introduced by long-range connections causes frustration, which gives rise to a spin-glass phase at low temperature. Monte Carlo simulations have been carried out to study the paramagnetic to spin-glass transition, as a function of the rewiring probability p, which measures the disorder strength. The transition temperature Tc goes down for increasing disorder, and saturates to a value Tc ~ 1.7 J for p > 0.4, J being the antiferromagnetic coupling. For small p and at low temperature, the energy increases linearly with p. In the strong-disorder limit p=1, this model is equivalent to a short-range +-J spin glass in random networks.