Spin Glasses

From a physical point of view, spin glasses, as dilute magnetic alloys, are very interesting systems. They are characterized by such features as exhibiting a new magnetic phase, where magnetic moments are frozen into disordered equilibrium orientations, without any long-range order. See for example [1] for general reviews, and also [2] for a very readable account about the physical properties of spin glasses. The experimental laboratory study of spin glasses is a very difficult subject, because of their peculiar properties. In particular the existence of very slowly relaxing modes, with consequent memory effects, makes difficult to realize the very basic physical concept of a system at thermodynamical equilibrium, at a given temperature. From a theoretical point of view some models have been proposed, which try to capture the essential physical features of spin glasses, in the frame of very simple assumptions. The basic model has been proposed by Edwards and Anderson [3] many years ago. It is a simple extension of the well known nearest neighbour Ising model. On a large region Λ of the unit lattice in d dimensions, we associate an Ising spin σ(n) to each lattice site n, and then we introduce a lattice Hamiltonian HΛ(σ, J) = − ∑