Glassy behaviour in a simple topological model

In this paper we study a simple, purely topological, cellular model which i s allowed to evolve through a Glauber-Kawasaki process. We find a non-therm odynamic transition to a glassy phase in which the energy (defined as the s quare 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 try a factor of the relaxation time t(r). This master curve can be fitted by a von Schweidler law in the late beta -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 exponen t of the power law and the von Schweidler law roughly agree with the relati onship predicted by mode-coupling theory. By defining a suitable response f unction, we find that the fluctuation-dissipation ratio is held until somet ime later than the appearance of the plateaux; non-monotonicity of the resp onse is observed after this ratio is broken, a feature which has been obser ved in other models with dynamics involving activated processes.