Ising model in small-world networks

TL;DR

This study investigates the phase transition behavior of the Ising model on small-world networks derived from 2D and 3D lattices, revealing mean-field characteristics and specific divergence patterns of heat capacity.

Contribution

It provides a detailed analysis of the ferromagnetic transition in small-world networks, highlighting the mean-field nature and divergence behavior as the disorder parameter varies.

Findings

Phase transition has mean-field character for any finite rewiring probability p.

Transition temperature and critical energy follow a power law in p for small p.

Heat capacity diverges logarithmically in 2D and as a power law in 3D as p approaches zero.

Abstract

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 p -> 0, the heat capacity at the transition temperature diverges logarithmically in two-dimensional (2D) networks and as a power law in 3D.