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

Abstract

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.

17 pages, 10 figures

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Cited by in corpus (11)

• Strong Disorder RG approach - a short review of recent developments
• Eigenvalue method to compute the largest relaxation time of disordered systems
• Duality symmetries and effective dynamics in disordered hopping models
• Random elastic networks : strong disorder renormalization approach
• Matching between typical fluctuations and large deviations in disordered systems : application to the statistics of the ground state energy in the SK spin-glass model
• Quenched-Vacancy Induced Spin-Glass Order
• Competition between quenched disorder and long-range connections: A numerical study of diffusion
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach
• Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules
• Anomalous diffusion in disordered multi-channel systems
• Chaotic Spin Correlations in Frustrated Ising Hierarchical Lattices