Ising model on a 2D additive Small-World Network

TL;DR

This study uses Monte Carlo simulations to analyze the Ising model on a 2D additive small-world network, revealing how the phase transition behavior shifts from regular lattice to small-world characteristics as the probability p varies.

Contribution

It introduces a detailed simulation of the Ising model on a 2D additive small-world network and explores the impact of random long-range connections on critical phenomena.

Findings

Identified a continuous phase transition between ferromagnetic and paramagnetic phases.

Constructed the phase diagram in temperature vs. probability p.

Observed a change in critical exponents with varying p.

Abstract

In this article, we have employed Monte Carlo simulations to study the Ising model on a two-dimensional additive small-world network (A-SWN). The system model consists of a LxL square lattice where each site of the lattice is occupied for a spin variable that interacts with the nearest neighbor and has a certain probability p of being additionally connected at random to one of its farther neighbors. The system is in contact with a heat bath at a given temperature T and it is simulated by one-spin flip according to the Metropolis prescription. We have calculated the thermodynamic quantities of the system, such as, the magnetization per spin m, magnetic susceptibility chi, and the reduced fourth-order Binder cumulant U as a function of T for several values of lattice size L and additive probability p. We also have constructed the phase diagram for the equilibrium states of the model in the plane T versus p showing the existence of a continuous transition line between the ferromagnetic F and paramagnetic P phases. Using the finite-size scaling (FSS) theory, we have obtained the critical exponents for the system, where varying the parameter p, we have observed a change in the critical behavior from the regular square lattice Ising model to A-SWN.