Mean-field theory of the Ashkin-Teller spin glass

Abstract

The Gaussian-distributed random-bond Ashkin-Teller model on a Cayley tree is studied in the limit of infinite coordination number. This study is based on the relationship between the properties of the system defined on the usual Cayley tree and those of the system defined on a related hierarchical tree, the so-called closed asymmetric tree (CAT). With exploration of the hierarchical nature of the CAT a real-space renormalization-group procedure is implemented to obtain the generalized Sherrington-Kirkpatrick (SK) equations. The phase diagrams in three particular cases are obtained by numerical analysis of the SK equations.