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
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 pc 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.
PACS: 61.43.-j – Disordered solids / 61.43.Fs – Glasses / 64.60.Ht – Dynamic critical phenomena
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000