Glassy behaviour in a simple topological model
Journal of Physics A: Mathematical and General 33:48 (2000) 8615-8625
Abstract:
In this paper we study a simple, purely topological, cellular model which is allowed to evolve through a Glauber-Kawasaki process. We find a non-thermodynamic transition to a glassy phase in which the energy (defined as the square of the local cell topological charge) fails to reach the equilibrium value below a characteristic temperature which is dependent on the cooling rate. We investigate a correlation function which exhibits ageing behaviour, and follows a master curve in the stationary regime when time is rescaled by a factor of the relaxation time tr. This master curve can be fitted by a von Schweidler law in the late β-relaxation regime. The relaxation times can be well fitted at all temperatures by an offset Arrhenius law. A power law can be fitted to an intermediate-temperature regime; the exponent of the power law and the von Schweidler law roughly agree with the relationship predicted by mode-coupling theory. By defining a suitable response function, we find that the fluctuation-dissipation ratio is held until sometime later than the appearance of the plateaux; non-monotonicity of the response is observed after this ratio is broken, a feature which has been observed in other models with dynamics involving activated processes.Continuous time dynamics of the thermal minority game.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 62:1 Pt A (2000) R9-R12
Abstract:
We study the continuous time dynamics of the thermal minority game. We find that the dynamical equations of the model reduce to a set of stochastic differential equations for an interacting disordered system with nontrivial random diffusion. This is the simplest microscopic description which accounts for all the features of the system. Within this framework, we study the phase structure of the model and find that its macroscopic properties strongly depend on the initial conditions.p>2 spin glasses with first-order ferromagnetic transitions
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 33:16 (2000) 3081-3091
A simple model of a glass with finite-range periodic interactions
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 33:50 (2000) L497-L502