Mean field solution of the Ising model on a Barabasi-Albert network

TL;DR

This paper derives a mean field solution for the Ising model on a Barabasi-Albert network, revealing an infinite critical temperature and a size-dependent effective critical temperature that aligns with recent numerical findings.

Contribution

It provides an analytical mean field framework for the Ising model on scale-free networks, highlighting the divergence of the critical temperature.

Findings

Critical temperature is infinite for the model.

Effective critical temperature increases logarithmically with system size.

Results agree with recent numerical simulations.

Abstract

The mean field solution of the Ising model on a Barabasi-Albert scale-free network with ferromagnetic coupling between linked spins is presented. The critical temperature $T_c$ for the ferromagnetic to paramagnetic phase transition (Curie temperature) is infinite and the effective critical temperature for a finite size system increases as the logarithm of the system size in agreement with recent numerical results of Aleksiejuk, Holyst and Stauffer.