Ising model on two connected Barabasi-Albert networks

TL;DR

This paper analyzes the phase behavior of the Ising model on two interconnected Barabasi-Albert networks, revealing phase transitions between parallel and antiparallel spin alignments, supported by analytical and numerical methods.

Contribution

It provides an analytical framework for understanding Ising model behavior on interconnected scale-free networks, a novel extension of previous single-network studies.

Findings

Two phases: parallel and antiparallel spin alignment.

Critical temperature difference vanishes with zero inter-network coupling.

Analytical predictions are confirmed by numerical simulations.

Abstract

We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.