Random Two-Body Interactions and Regular Many-Body Physics

Y.M. Zhao, A. Arima, N. Yoshinaga

Yoichiro Hashizume, Masuo Suzuki

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.

Georg Wolschin

Lingzhen Guo

Y. M. Zhao

In this paper we present a brief discussion on regular structures of many‐body systems generated from random two‐body interactions. In particular, we discuss the famous problem of spin zero ground state dominance, regularities of energy centroids and collectivity in the presence of random interactions.

Y. M. Zhao, A. Arima, Naotaka Yoshinaga +1 more

2 Regularities of the ground states in the presence of random interactions 9 2.1 Fermions in a single-j shell........................ 10