Prof. David Sherrington FRS

Abstract:

A discussion is presented of the effects of stochasticity in the decision-making of agents in the minority game. Both simulational and analytic results are reported and discussed for both additive and multiplicative noise. As a function of the ratio d of information dimension to number of agents a phase transition separates a low d non-ergodic phase from a high d ergodic phase. For additive noise the critical d, is temperature-independent but for multiplicative noise d(c) (T) decreases with T. Additive noise does not affect the asymptotic behaviour for d > d(c) but is relevant below d(c). Multiplicative noise has consequence for all d. (C) 2002 Elsevier Science B.V. All rights reserved.

Abstract:

We report a study of a series of simple model systems with only non-interacting Hamiltonians, and hence simple equilibrium thermodynamics, but with constrained dynamics of a type initially suggested by foams and idealized covalent glasses. We demonstrate that macroscopic dynamical features characteristic of real and more complex model glasses, such as two-time decays in energy and auto-correlation functions, arise from the dynamics and we explain them qualitatively and quantitatively in terms of annihilation-diffusion concepts and theory. The comparison is with strong glasses. We also consider fluctuation-dissipation relations and demonstrate subtleties of interpretation. We find no FDT breakdown when the correct normalization is chosen.