Critical exponents from power spectra

Abstract

We have simulated the two- and three-dimensional Ising models at their respective critical points with a conventional Monte Carlo algorithm. From the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz = 2.16–2.19 andz = 2.05, in agreement with the results quoted in the literature. We have also studied the power spectrum for the Kardar-Parisi-Zhang and Sun-Guo-Grant equations describing interface dynamics. Arguments similar to what was recently used to conclude thatz = 4 -η for model B in critical dynamics were applied to the Sun-Guo-Grant growth model and the known exact values for the roughening and dynamic exponents were obtained. From an analysis of the corresponding power spectrum in self-organized critical sand models one obtains a recently proposed hyperscaling relation.