Spin dynamics and glassy relaxation on fractals and percolation structures
- 1 January 1985
- journal article
- Published by EDP Sciences in Journal de Physique
- Vol. 46 (11) , 1837-1842
- https://doi.org/10.1051/jphys:0198500460110183700
Abstract
Single-spin-flip dynamics of discrete spin models on fractals and percolation structures is studied within the framework of a low temperature approach. Using a scaling theory we show that, in general, the energy barrier for overturning a finite cluster of s spins scales as In s. The probability distribution of the energy barriers for percolation clusters is argued to be given by the extreme-value distribution. The resulting long time relaxational dynamics so obtained is a stretched exponential with a temperature dependent exponent. Our results lead to a natural formulation of a new dynamic scaling hypothesis and are discussed in relation with the so-called glassy dynamicsKeywords
This publication has 11 references indexed in Scilit:
- Critical Ising Spin Dynamics near the Percolation ThresholdPhysical Review Letters, 1985
- Low-Frequency Relaxation in Ising Spin-GlassesPhysical Review Letters, 1985
- Energy barriers of the Ising model on percolation clusters : a numerical studyJournal de Physique Lettres, 1985
- Building Blocks of Percolation Clusters: Volatile FractalsPhysical Review Letters, 1984
- Relaxations in spin glasses: Similarities and differences from ordinary glassesJournal of Applied Physics, 1984
- Static and dynamic magnetic response of spin-glass models with short-range interactionsPhysical Review B, 1984
- Geometric Implementation of Hypercubic Lattices with Noninteger Dimensionality by Use of Low Lacunarity Fractal LatticesPhysical Review Letters, 1983
- Thermal Phase Transition of the Dilute-State Potts and-Vector Models at the Percolation ThresholdPhysical Review Letters, 1981
- Effect of disorder on relaxation in the one-dimensional Glauber modelJournal of Statistical Physics, 1980
- Some statistical aspects of relaxation time distributionsPhysica, 1962