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To describe the equilibrium properties of disordered systems and the possibleemergence of various 'phases' at low temperature, we adopt here the 'brokenergodicity' point of view advocated in particular by Palmer [Adv. Phys. 31, 669(1982)] : the aim is then to construct the valleys of configurations thatbecome separated by diverging barriers and to study their relative weights, aswell as their internal properties. To characterize the slow non-equilibriumdynamics of disordered systems, we have recently introduced in [C. Monthus andT. Garel, J. Phys. A 41, 255002 (2008) and arxiv:0804.1847] a strong disorderrenormalization procedure in configuration space, based on the iterativeelimination of the smallest barrier remaining in the system. In the presentpaper, we show how this renormalization procedure allows to construct thelongest-lived valleys in each disordered sample, and to obtain theirfree-energies, energies and entropies. This explicit RG formulation is verygeneral since it can be defined for any master equation, and it gives newinsights into the main ingredients of the droplet scaling picture. As anapplication, we have followed numerically the RG flow for the case of adirected polymer in a two-dimensional random medium to obtain histograms of thefree-energy, entropy and energy differences between the two longest-livedvalleys in each sample.

Equilibrium of disordered systems : constructing the appropriate valleys in each sample via strong disorder renormalization in configuration space