Linear and Nonlinear Critical Slowing Down in the Kinetic Ising Model

Recently, it .was presented that the critical singularity of the linear and nonlinear relaxation time may be different in the kinetic Ising model by using the mean :field approximation (MFA) Y Both critical singularities have been asserted to be identical in ergodic systems so far by an intuitive expectation. 2> In this letter, as a further example we consider the kinetic Ising modeP> on a Bethe lattice. Such a condition makes the high-temperature-expansion method4> simple, and furthermore the equilibrium properties are well understood ;5> a=O, 13=1/2, r=1, for usual critical indices. It will be desirable for our purpose to use the large coordination number z. In our case we set z=6. From now on we adopt the same notations as in Ref. 4) except that -r=1, m=l. Thus we write the master equation as