IRREVERSIBILITY IN HEISENBERG SPIN SYSTEMS .3. KINETIC EQUATIONS FOR AUTOCORRELATION FUNCTION AT FINITE TEMPERATURE

Recently the authors have derived kinetic equations describing the behavior of the spin autocorrelation function q(t) in a Heisenberg system at infinite temperature. In the present paper, this derivation is extended to finite temperatures (above the critical point). It is shown that, in the Weiss limit where the number of neighbors Z, the effects of the equilibrium (Ornstein-Zernicke) correlations present in the system at the initial time can be entirely incorporated within an effective temperature-dependent interaction which governs the temporal behavior of the autocorrelation function (af). A non-Markoffian kinetic equation is obtained in which the kernel is highly nonlinear in the complete af q(t); this contrasts with the infinite-temperature case, where the kernel was a functional of the direct af only. This new feature leads to simple approximations near the critical point, as will be discussed in detail in the next paper of this series. © 1969 The American Physical Society.