Ajay, ; Palmer, RG, *Simulation of a toy model with constrained dynamics*,
Journal of Physics A: Mathematical and General, vol. 23 no. 11
(1990),
pp. 2139-2145 [doi] .
**Abstract:**

*We 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. We 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. We 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. The stretched exponential behaviour in the short-time regime is a natural consequence of the constrained dynamics. © 1990 IOP Publishing Ltd.*