Mean-Field Theory of Randomly Frustrated Systems with Finite Connectivity

Abstract

We study spin systems–ferromagnets, spin glasses, graph bipartitioning–on random lattices with a finite connectivity. New features of spin glass theory are pointed out, such as the influence of the shape of the distribution of exchange couplings. For the bipartitioning of random graphs with fixed connectivity, the results of the replica symmetric solution give a good first approximation of the ground-state energy.