Comment on "Thermal model for adaptive competition in a market -: Cavagna et al. reply
PHYSICAL REVIEW LETTERS 85:23 (2000) 5009-5009
Competition between glassiness and order in a multispin glass.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 60:3 (1999) R2460-R2463
Abstract:
A mean-field multispin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet, and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.Glass transition in self-organizing cellular patterns
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 32:41 (1999) 7049-7056
Phase diagram and storage capacity of sequence storing neural networks
ADV NEUR IN 11 (1999) 211-217
Abstract:
We solve the dynamics of Hopfield-type neural networks which store sequences of patterns, close to saturation. The asymmetry of the interaction matrix in such models leads to violation of detailed balance, ruling out an equilibrium statistical mechanical analysis. Using generating functional methods we derive exact closed equations for dynamical order parameters, viz. the sequence overlap and correlation and response functions, in the limit of an infinite system size. We calculate the time translation invariant solutions of these equations, describing stationary limit-cycles, which leads to a phase diagram. The effective retarded self-interaction usually appearing in symmetric models is here found to vanish, which causes a significantly enlarged storage capacity of alpha(c) approximate to 0.269, compared to alpha(c) approximate to 0.139 for Hopfield networks storing static patterns. Our results are tested against extensive computer simulations and excellent agreement is found.Thermal model for adaptive competition in a market
PHYSICAL REVIEW LETTERS 83:21 (1999) 4429-4432