Rigorous Inequalities for the Spin-Relaxation Function in the Kinetic Ising Model

Abstract

Rigorous lower bounds are established for the spin-relaxation function in kinetic Ising models. A recently published estimate, based on Monte Carlo calculations, that the spin autocorrelation time is proportional to $T_c$ in two dimensions, near the critical temperature ${|T-T_c|}^{-1\mathrm{}}$, is shown to be incorrect because it violates these inequalities.