Statics and Dynamics of Antiferromagnetic Ising System on a Triangular Lattice. I

Abstract

The Ising model on a triangular lattice with antiferromagnetic nearest neighbor and ferromagnetic next nearest neighbor interactions is investigated by treating the master equation by molecular field approximation(MFA) and the cluster decoupling approximation(CDA). For the fully frustrated case, CDA gives no phase transition in contrast with the MFA result which gives the finite Néel temperature. The change of states (i.e., phase transition) is explained by words of bifurcation theory and the relaxation process is investigated by studying the flow in the space of sublattice magnetizations in each approximation.