NEW RANDOM ORDERED PHASE IN ISOTROPIC MODELS WITH MANY-BODY INTERACTIONS

Abstract

In this study, we have found a new random ordered phase in isotropic models with many-body interactions. Spin correlations between neighboring planes are rigorously shown to form a long-range order, namely coplanar spin-pair order, using a unitary transformation, and the phase transition of this new order has been analyzed on the bases of the mean-field theory and correlation identities. In the systems with regular 4-body interactions, the transition temperature T c is obtained as T c = (z-2)J/k B , and the field conjugate to this new order parameter is found to be H2. In contrast, the corresponding physical quantities in the systems with random 4-body interactions are given by [Formula: see text] and H4, respectively. Scaling forms of order parameters for regular or random 4-body interactions are expressed by the same scaling functions in the systems with regular or random 2-body interactions, respectively. Furthermore, we have obtained the nonlinear susceptibilities in the regular and random systems, where the coefficient χnl of H3 in the magnetization shows positive divergence in the regular model, while the coefficient χ7 of H7 in the magnetization shows negative divergence in the random model.