Critical slowing down in the two-dimensional one-spin-flip Ising model

Abstract

We extend a previous Monte Carlo investigation to include the relaxation times associated with the first time moment of the relaxation function and of the relaxation function squared. Moreover, we introduce, in addition to the order-parameter and energy-relaxation functions, that of the order parameter squared. The asymptotic temperature dependence of the associated relaxation times is found to support the validity of rather extended dynamic scaling hypotheses, predicting that all the associated exponents of slowing down are equal and symmetric with respect to Tc. We also derive various exact lower bounds and inequalities for these relaxation times and exponents. Our numerical data are found to be consistent with these exact results. © 1974 The American Physical Society.