Comparison of the path-probability method (PPM) with the master-equation method (MEM) is extended to a higher degree of approximation (triangle approximation) for the kinetics of Ising ferromagnetism. The evolution equations of the averages and of the fluctuations around them are derived analytically in this high degree of approximation for the first time for both methods. Contrary to the case of pair approximation presented in Ishikawa et al. (the preceding paper), it was not possible to bring the evolution equations derived by the MEM into a complete agreement with those by the PPM even with the use of the most reasonable closure relations.

• Received 9 December 1985

DOI:https://doi.org/10.1103/PhysRevA.33.4171