Comment on "Ising model on a small world network"

Abstract

In the recent study of the Ising model on a small-world network by A. Pȩkalski [Phys. Rev. E {\bf 64}, 057104 (2001)], a surprisingly small value of the critical exponent $β\approx 0.0001$ 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. Pȩkalski but in accord with other existing studies.

to be published in PRE