2003/02/28 by Jesper Dall, Paolo Sibani · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Attractor #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Condensed matter physics #Distribution (mathematics) #Energy landscape #Gaussian #Geometry #Materials science #Mathematics #Maxima and minima #Metastability #Physics #Poisson distribution #Quantum mechanics #Range (aeronautics) #Relaxation (psychology) #Scaling #Spin glass #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2003-00340-y
published as Eur.Phys.J.B 36 (2) 233-243 (2003) · 16 pages, 7 figures, RevTex v2: Corrections to argument about mean residence time in a valley v3: Corrected version, with updated figures
arxiv created 2003/08/21 · openalex publication_date 2003/11/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
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 tw 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.