Monte Carlo study of relaxation and diffusion in glassy systems

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Abstract
Using a combination of Monte Carlo and analytical techniques we present an analysis of the random-walk problem of a particle diffusing in a system with energetic disorder. The particle is allowed to hop anywhere in the lattice and the rates vary exponentially with distance. We consider the number of new sites visited, the average energy, and diffusivity as a function of time and temperature. Deviations from mean-field theories are most pronounced at low temperatures when the relaxation can ‘‘freeze’’ at dead ends and deep traps. The Monte Carlo data can be summarized in terms of generalized analytical relations with a wide range of applications.