Gibbs vs. Non-Gibbs in the Equilibrium Ensemble Approach to Disordered Systems
2004, v.10, Issue 3, 523-545
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 low-concentration 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.
Keywords: disordered systems,non-Gibbsianness,variational bounds,Morita method