We describe the salient ideas of the equilibrium ensemble approach to disordered systems, paying due attention to the appearance of non-Gibbsian measures. A canonical scheme of approximations – constrained annealing – is described and characterised in terms of a Gibbs ’ variational principle for the free energy functional. It provides a family of increasing exact lower bounds of the quenched free energy of disordered systems, and is shown to avoid the use of non-Gibbsian measures. The connection between the equilibrium ensemble approach and conventional lowconcentration expansions or perturbation expansions about ordered reference systems is also explained. Finally applications of the scheme to a number of disordered Ising models and to protein folding are briefly reviewed. AMS subject classification: 82B05 Classical equilibrium statistical mechanics 82B44 Disordered systems Key words: Morita method, disordered systems, variational bounds, non-Gibbsiannes
