The Ising model in small-world networks generated from two- and three-dimensional regular lattices has been studied. Monte Carlo simulations were carried out to characterize the ferromagnetic transition appearing in these systems. In the thermodynamic limit, the phase transition has a mean-field character for any finite value of the rewiring probability p, which measures the disorder strength of a given network. For small values of p, both the transition temperature and critical energy change with p as a power law. In the limit $\overrightarrow{p}0,$ the heat capacity at the transition temperature diverges logarithmically in two-dimensional (2D) networks and as a power law in 3D.

• Received 21 January 2002

DOI:https://doi.org/10.1103/PhysRevE.65.066110