Kinetic lattice gas model of collective diffusion in a one-dimensional system with long-range repulsive interactions

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
Magdalena A. Załuska-Kotur ◽  
Zbigniew W. Gortel
Keyword(s):  
Long Range ◽  
Lattice Gas ◽  
Lattice Gas Model ◽  
Dimensional System ◽  
One Dimensional ◽  
Repulsive Interactions ◽  
Kinetic Lattice

Diffusion simulation with a deterministic one-dimensional lattice-gas model

1992 ◽  
Vol 68 (3-4) ◽  
pp. 563-573 ◽  
Author(s):  
Y. H. Qian ◽  
D. d'Humi�res ◽  
P. Lallemand
Keyword(s):  
Lattice Gas ◽  
Lattice Gas Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Diffusion Simulation

AGING IN A ONE-DIMENSIONAL EDWARDS–ANDERSON SPIN GLASS MODEL WITH LONG-RANGE INTERACTIONS

2003 ◽  
Vol 14 (03) ◽  
pp. 257-265 ◽  
Author(s):  
MARCELO A. MONTEMURRO ◽  
FRANCISCO A. TAMARIT
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Dynamical Behavior ◽  
Mean Field ◽  
Dimensional System ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Glass Model ◽  
The One ◽  
Aging Phenomena

In this work we study, by means of numerical simulations, the out-of-equilibrium dynamics of the one-dimensional Edwards–Anderson model with long-range interactions of the form ± Jr-α. In the limit α → 0 we recover the well known Sherrington–Kirkpatrick mean-field version of the model, which presents a very complex dynamical behavior. At the other extreme, for α → ∞ the model converges to the nearest-neighbor one-dimensional system. We focus our study on the dependence of the dynamics on the history of the sample (aging phenomena) for different values of α. The model is known to have mean-field exponents already for values of α = 2/3. Our results indicate that the crossover to the dynamic mean-field occurs at a value of α < 2/3.

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