Statics and dynamics of the ten-state mean-field Potts glass model: a Monte Carlo study

Abstract

We investigate by means of Monte Carlo simulations the fully connectedp-state Potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the, exactly known, behaviour of the system in the thermodynamic limit. Using p = 10 we are able to study the equilibrium dynamics for system sizes as large as N = 2560. We find that the static quantities, such as the energy, the entropy, the spin glass susceptibility as well as the distribution of the order parameter P(q) show very strong finitesize effects. From P(q) we calculate the fourth-order cumulant g4(N, T ) and the Guerra parameter G(N, T ) and show that these quantities cannot be used to locate the static transition temperature for the system sizes investigated. Also the spin-autocorrelation function C(t) shows strong finite-size effects in that it does not show a plateau even for temperatures around the dynamical critical temperature TD . We show that the dependence on N and T of the α-relaxation time can be understood by means of a dynamical finite-size scaling ansatz. C(t) does not obey the time–temperature superposition principle for temperatures around TD , but does so for significantly lower T . Finally we study the relaxation dynamics of the individual spins and show that their dependence on time depends strongly on the chosen spin, i.e. that the system is dynamically very heterogeneous, which explains the non-exponentiality of C(t). PACS numbers: 05.50.+q, 05.10.Ln, 75.10.-b

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Cite this paper

@inproceedings{Brangian2002StaticsAD, title={Statics and dynamics of the ten-state mean-field Potts glass model: a Monte Carlo study}, author={Claudio Brangian and Walter Kob and Kurt Binder}, year={2002} }