New Random Ordered Phase in Isotropic Models with Many-body Interactions

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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 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 Tc is obtained as Tc=(z-2)J/kB, 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 Tc=√z-2J/kB 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.