Eur. Phys. J. B 18, 513-518 (2000)
https://doi.org/10.1007/s100510070041

Stretched exponential relaxation on the hypercube and the glass transition

¹ Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS, Brazil
² Centro de Ciências Exatas e da Terra, Unisinos Av. Unisinos, 950 93022-000, São Leopoldo, RS, Brazil
³ Laboratoire des Verres, Université de Montpellier II, 34095 Montpellier Cedex 5, France
⁴ Laboratoire de Physique des Solides, Université Paris Sud, 91405 Orsay, France

Corresponding author: ^a lemke@exatas.unisinos.br

Received: 16 June 2000
Revised: 13 October 2000
Published online: 15 December 2000

Abstract

We study random walks on the dilute hypercube using an exact enumeration Master equation technique, which is much more efficient than Monte Carlo methods for this problem. For each dilution p the form of the relaxation of the memory function q(t) can be accurately parametrized by a stretched exponential over several orders of magnitude in q(t). As the critical dilution for percolation p_c is approached, the time constant tends to diverge and the stretching exponent drops towards 1/3. As the same pattern of relaxation is observed in a wide class of glass formers, the fractal like morphology of the giant cluster in the dilute hypercube appears to be a good representation of the coarse grained phase space in these systems. For these glass formers the glass transition may be pictured as a percolation transition in phase space.