Comment on "Ising model on a small world network"

TL;DR

This paper re-examines the Ising model on a small-world network, using extensive Monte Carlo simulations to clarify the nature of its phase transition, and finds it to be of mean-field type contrary to previous findings.

Contribution

The study provides a comprehensive Monte Carlo analysis confirming the mean-field nature of the phase transition in the Ising model on small-world networks.

Findings

Phase transition is of mean-field type.

Contradicts previous results of a non-standard critical exponent.

Supports existing studies on similar models.

Abstract

In the recent study of the Ising model on a small-world network by A. P\c{e}kalski [Phys. Rev. E {\bf 64}, 057104 (2001)], a surprisingly small value of the critical exponent $\beta \approx 0.0001$ has been obtained for the temperature dependence of the magnetization. We perform extensive Monte Carlo simulations of the same model and conclude, via the standard finite-size scaling of various quantities,that the phase transition in the model is of the mean-field nature, in contrast to the work by A. P\c{e}kalski but in accord with other existing studies.