A mean-field renormalisation-group approach to Ising andq=3-state Potts models with long-range interactions in one dimension

2017 ◽  
Vol 481 ◽  
pp. 34-40
Author(s):  
C.E.K. Soares ◽  
J. Ricardo de Sousa ◽  
N.S. Branco
Keyword(s):  
Long Range ◽  
Mean Field ◽  
Renormalisation Group ◽  
One Dimension ◽  
Group Approach ◽  
Potts Models ◽  
Long Range Interactions

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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