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Abstract:

A brief review is presented of the minority game, a simple frustrated many-body system stimulated by considerations of a market of competitive speculative agents. Its cooperative behaviour exhibits phase transitions and both ergodic and non-ergodic regimes. It provides novel challenges to statistical physics, reminiscent of those of mean-field spin glasses. (C) 2007 Elsevier B.V. All rights reserved.

Abstract:

Numerical results up to the 42nd order of replica-symmetry breaking (RSB) are used to predict the singular structure of the Sherrington-Kirkpatrick spin glass at T=0. We confirm predominant single parameter scaling and derive corrections for the T=0 order function q(a), related to a Langevin equation with pseudotime 1/a. a=0 and a=infinity are shown to be two critical points for infinity-RSB, associated with two discrete spectra of Parisi block size ratios, attached to a continuous spectrum. Finite-RSB-size scaling, associated exponents, and T=0-energy are obtained with unprecedented accuracy.

Abstract:

A brief personal perspective is given of issues, questions, formulations, methods, some answers and selected extensions posed by the spin glass prob- lem, showing how considerations of an apparently insignificant and practically unimportant group of metallic alloys stimulated an explosion of new insights and opportunities in the general area of complex many-body systems and still is doing so. and selected ...