On the stability of randomly frustrated systems with finite connectivity

Abstract

The authors study dilute spin systems with finite connectivity, i.e. Viana-Bray random bond systems, near zero temperature. The authors give a stationary free energy in terms of a global order parameter g together with the equation of motion for g and the stability matrix. For the case where replica symmetry is not broken, they diagonalise the stability matrix around the ansatz given by Mezard and Parisi (1985), and Kanter and Sompolinsky (1987), close to the point of percolation ( alpha =1) and for small admixtures of antiferromagnetic bonds. They find that the replica symmetric ansatz is unstable in the spin glass phase and in part of the ferromagnetic phase.