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 a level of a pure state, the nonlinear susceptibility is de- rived. When a cluster of pure states is considered, all the known results of the one-step replica-symmetry breaking approach are easily reproduced. Besides, the nonlinear susceptibility and the stability conditions are obtained and re- lated 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 71 where the quadrupolarization and the quadrupo- lar glass order parameters are nonzero and finite. Tlis may be interpreted as a signal of a glassy phase transition not in the Landau sense.
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