Prof. David Sherrington FRS

Abstract:

A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to analytic results for the model rather than discussions of its relevance in real-world situations. (c) 2006 Elsevier B.V. All rights reserved.

Abstract:

A brief review is given of the minority game, an idealized model stimulated by a market of speculative agents, with emphasis on its statistical physics.

Abstract:

Using numerical self-consistent solutions of a sequence of finite replica symmetry breakings (RSB) and Wilson's renormalization group but with the number of RSB steps playing a role of decimation scales, we report evidence for a nontrivial T-->0 limit of the Parisi order function q(x) for the Sherrington-Kirkpatrick spin glass. Supported by scaling in RSB space, the fixed point order function is conjectured to be q*(a)=sqrt[pi]/2 a/xi erf(xi/a) on 0 a at T =0 and xi approximately 1.13+/-0.01. Xi plays the role of a correlation length in a-space. q*(a) may be viewed as the solution of an effective 1D field theory.