  To describe the equilibrium properties of disordered systems and the possible
emergence of various 'phases' at low temperature, we adopt here the 'broken
ergodicity' point of view advocated in particular by Palmer [Adv. Phys. 31, 669
(1982)] : the aim is then to construct the valleys of configurations that
become separated by diverging barriers and to study their relative weights, as
well as their internal properties. To characterize the slow non-equilibrium
dynamics of disordered systems, we have recently introduced in [C. Monthus and
T. Garel, J. Phys. A 41, 255002 (2008) and arxiv:0804.1847] a strong disorder
renormalization procedure in configuration space, based on the iterative
elimination of the smallest barrier remaining in the system. In the present
paper, we show how this renormalization procedure allows to construct the
longest-lived valleys in each disordered sample, and to obtain their
free-energies, energies and entropies. This explicit RG formulation is very
general since it can be defined for any master equation, and it gives new
insights into the main ingredients of the droplet scaling picture. As an
application, we have followed numerically the RG flow for the case of a
directed polymer in a two-dimensional random medium to obtain histograms of the
free-energy, entropy and energy differences between the two longest-lived
valleys in each sample.
