Comment on “Ising model on a small world network”

Abstract

In the recent study of the Ising model on a small world network by Pȩkalski [Phys. Rev. E 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 Pȩkalski, but in accordance with other existing studies.