Renormalisation group theory of spin glasses

Abstract

The renormalisation group scheme for the thermodynamic theory of metastable states in spin glasses is proposed. On the basis of the hierarchical organisation of states in spin glasses, it is possible to calculate an effective distribution functional of spin-spin interactions with increasing scale in a phase space. For the Sherrington-Kirkpatrick model (1975), its explicit form has been found both above and below the phase transition point. Below the phase transition point the system is shown to be 'trapped' in a finite region of the phase space which corresponds to one of the ancestor states of the hierarchical tree.