Cavity-fields approach to a simple model of axial quadrupolar glass.

Abstract

A simple infinite-range model of axial quadrupolar glass is investigated within the cavity-fields approach inside a pure state and a cluster of pure states. Working at the level of a pure state, the Thouless-Anderson-Palmer (TAP)--like equations and the nonlinear susceptibility are derived and the thermodynamic stability conditions are obtained in a transparent physical way. At this first stage, the cavity-fields results agree with those previously achieved within the replica-symmetric scheme. At the second stage of the cavity method, where a cluster of pure states is considered, all the known results of the one-step replica-symmetry breaking approach are easily reproduced. Besides the TAP-like equations for the quadrupolar ancestor, the nonlinear susceptibility and the stability conditions are obtained and related numerical results are presented. In this way the stability range of the replica-symmetry breaking solution, quite difficult to be derived within the replica method, is established on the purely physical ground. An interesting feature is that, at any considered stage, the nonlinear susceptibility diverges at a given temperature ${\mathit{T}}_{\mathit{c}}$ where the quadrupolarization and the quadrupolar glass order parameters are nonzero and finite. This may be interpreted as a signal of a glassy phase transition not in the Landau sense. \textcopyright{} 1996 The American Physical Society.