Kinetics of the stochastic ising chain in a two-flip model

Abstract

The exact solution is presented of a stochastic model for the cyclic Ising chain of N spins with nearest-neighbour interactions in the absence of a magnetic field. In each transition two neighbouring spins simultaneously change their states with transition probability determined by the state of their neighbours and the temperature of a heat bath. A set of spin operators is constructed whose average values decay to their equilibrium values exponentially in time. Relaxation of the Fourier components of magnetization and energy density is treated in detail.