Simulation of a toy model with constrained dynamics

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Abstract
The authors study a sliding block model incorporating constraints in an attempt to understand the slower than exponential relaxation observed in glassy systems. Blocks are free to slide along the axes of a regular lattice but cannot interpenetrate. They simulate two-dimensional L*L lattices with L=8, 16, 32 and 64 and different number of vacancies. Three-dimensional L*L*L lattices with L=4, 8, 16 and 32 and one vacancy are also studied. They find the existence of three time regimes for relaxation towards complete disorder, in both two and three dimensions. In the short-time regime the relaxation follows a stretched exponential law; in the intermediate-time regime there is a t behaviour; and in the long-time regime the relaxation is exponential. In the intermediate- and long-time regimes the results agree well with the theoretical results of Brummelhuis and Hilhorst (1988). The stretched exponential behaviour in the short-time regime is a natural consequence of the constrained dynamics.