scholarly journals The one-dimensional Potts model with long-range interactions: a renormalization group approach

1997 ◽  
Vol 30 (10) ◽  
pp. 3345-3361 ◽  
Author(s):  
Sergio A Cannas ◽  
Aglaé C N de Magalhães
Keyword(s):  
Renormalization Group ◽  
Long Range ◽  
Potts Model ◽  
Group Approach ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Renormalization Group Approach ◽  
The One

scholarly journals Renormalization Group Approach to a One-Dimensional Cooperative T–e Jahn-Teller System

1977 ◽  
Vol 32 (1) ◽  
pp. 111-112
Author(s):  
S. Brühl ◽  
E. Sigmund
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
Ising Model ◽  
Linear Chain ◽  
Group Approach ◽  
One Dimensional ◽  
Renormalization Group Approach ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
The One

Abstract A linear chain of T-e molecules exhibiting the cooperative Jahn-Teller effect is considered. Following Nauenberg's1 treatment of the one-dimensional Ising model a renormalization group approach is used. The series-expansion of the free energy is put into a closed form.

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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