1/f noise in the Ising model

Abstract

We simulate the N-spin critical Ising model on a square lattice using Glauber dynamics and consider the typical one-unit time equal to N single-spin-flip attempts. The divergence of correlation time with the linear extent of the system results in critical slowing down, a challenge to equilibration because the spin configurations generated in such a way are temporally correlated. We examine temporal correlations in the number of accepted spin flips and show a signature of nontrivial long-time correlation of a logarithmically decaying form, or the corresponding power spectral density follows canonical 1/f noise.