We show how to derive equations for the local-effective-field distribution on a Bethe lattice (with appropriate boundary conditions) or on a random lattice with fixed (or average) finite connectivity when many thermodynamic states coexist. The method generalizes the cavity method to the finite-connectivity case and exhibits the correct equations for the instantaneous magnetic field at a given site. A comparison with previous results of Mottishaw and Thouless near the spin-glass transition is made.

• Received 30 October 1990

DOI:https://doi.org/10.1103/PhysRevB.43.8148