Antiferromagnetic Ising model in small-world networks

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 T_c goes down for increasing disorder, and saturates to a value T_c≈1.7J 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.