Exploring Valleys of Aging Systems: The Spin Glass Case

Abstract

We present a statistical method for complex energy landscape exploration which provides information on the metastable states--or valleys--actually explored by an unperturbed aging process following a quench. Energy fluctuations of record size are identified as the events which move the system from one valley to the next. This allows for a semi-analytical description in terms of log-Poisson statistics, whose main features are briefly explained. The bulk of the paper is devoted to thorough investigations of Ising spin glasses with Gaussian interactions of both short and long range, a well established paradigm for glassy dynamics. Simple scaling expressions with universal exponents for (a) barrier energies, (b) energy minima, and (c) the Hamming distance as a function of the valley index are found. The distribution of residence time inside valleys entered at age $t_w$ is investigated, along with the distribution of time at which the global minimum inside a valley is hit. Finally, the correlations between the minima of the landscape are presented. The results fit well into the framework of available knowledge about spin glass aging. At the same time they support a novel interpretation of thermal relaxation in complex landscapes with multiple metastable states. The marginal stability of the attractors selected is emphasized and explained in terms of geometrical properties of the landscape.