Time-correlation functions and critical relaxation in a class of one-dimensional stochastic spin systems

Abstract

The kinetics of the spin 1/2Ising chain is studied for a class of master equations describing transitions in the spin system owing to interactions with a heat bath. The case in which only transitions of n successive spins are allowed is called the n-flip model. The time-correlation functions for energy density and magnetization are calculated exactly in the limit of an infinite chain for all values of n. The effect of critical slowing-down near temperature T = O is studied and it is shown that the critical exponents characterizing the divergence of the relaxation times of energy and magnetization are independent of n.