The Cavity Method in the Mean Field Spin Glass Model. Functional Representations of Thermodynamic Variablesz

We consider the Sherrington-Kirkpatrick mean eld model for spin glasses and show how the cavity method can be exploited for constructing functional representations of the ther-modynamic variables, in terms of functional order parameters. One representation is based on a functional order parameter of Parisi type. By assuming that the functional order parameter does not depend on the strength of interaction of the added spin with the cavity, we show how to derive all properties found in the frame of the replica symmetry breaking method. The second representation introduces a density distribution on the interval 0; 1] as a functional order parameter. All thermodynamic quantities can be expressed through it. The connection between the two representations will be discussed elsewhere.