CONTROLLED RANDOMNESS AND FRUSTRATION OF THE MANY-BODY INTERACTIONS

Abstract

On the Ising spin systems constructed with four-body interactions, there appears the "spin-pair ordered phase" or "spin-pair glass phase" in a certain temperature. Especially, the random four-body models include the frustration and the spin-pair glass phase appears in those models. This frustration may play an important role of spin-pair glass transitions, similarly to the case of ordinary spin-glass transitions. In this study, we clarify the way to discriminate quantitatively "frustrated unit cells" from "nonfrustrated ones" on the random four-body models. Then we introduce a parameter to control the frustration in the Ising spin systems with random four-body interactions. This parameter enables us to analyze the frustration continuously in many-body models. Thus we have analyzed the phase transitions and obtained phase diagrams using the frustration parameter. These interesting phase diagrams show that there appear the spin-pair ordered phases even on the completely frustrated models. This result is essentially different from the random two-body models, namely spin-glass models (there appears no ferromagnetic phase in the fully frustrated spin-glass models, which correspond to the Villain models).