LIQUID-STATE METHODS FOR RANDOM-MEDIA .2. SPIN-GLASSES

The continuum replica method allows one to use equilibrium liquid-state theory to treat those nonequilibrium systems in which the quenched and annealed degrees of freedom correspond to distinct subsets of the particles in the system. In this paper, we provide a new generalization of the replica method that applies to a much larger class of continuum models. This involves using methods from the theory of chemical association to represent a particle as a bound state of pseudoparticles of different types or "species," each of which carries some of the degrees of freedom of the particle. We use this method to study a realistic continuum spin glass. In particular, we show how to construct thermodynamic perturbation theory for the correlation functions of the system. We also show in detail how to apply association methods to study models of growth and aggregation treating, in particular, the Eden model and self-avoiding walks (SAWs).