Replica Symmetry Breaking and the Spin-Glass on a Bethe Lattice

We study the spin-glass on a Bethe lattice using replicas. The problem is to find the fixed point of an iterative map in a 2 n -dimensional space as n approaches zero. We show that in the high-temperature phase the fixed point is replica symmetric, but in the spin-glass phase this becomes unstable. Making the Parisi ansatz we show that the overlap function P ( q ) has the same form as in the SK model.