Ergodicity breaking in a mean field Potts glass: A Monte Carlo investigation

We use Monte Carlo simulations, single spin-flip as well as parallel tempering techniques to investigate the 10-state fully connected Potts glass for system sizes of up to N = 2560. We find that the alpha-relaxation shows a strong dependence on N and that for the system sizes considered the system remains ergodic even at temperatures below T-D, the dynamical critical temperature for this model. However, if one uses the data for the finite size systems, such as the relaxation times or the time dependence of the spin autocorrelation function, and extrapolates them to the thermodynamic limit, one finds that they are indeed compatible with the results for N = infinity (which are known from analytical calculations) if the extrapolation is done in the correct way. At low temperatures we find that relaxation times tau diverge like exp(c (.) N-1/2). (C) 2002 Elsevier Science B.V. All rights reserved.