Onsager reaction field theory of the one-dimensional ferromagnet with long-range interactions

1996 ◽  
Vol 53 (9) ◽  
pp. 5123-5124 ◽  
Author(s):  
A. S. T. Pires
Keyword(s):  
Field Theory ◽  
Long Range ◽  
One Dimensional ◽  
Reaction Field ◽  
Long Range Interactions ◽  
The One

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.

scholarly journals Coexistence of coarsening and mean field relaxation in the long-range Ising chain

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Federico Corberi ◽  
Alessandro Iannone ◽  
Manoj Kumar ◽  
Eugenio Lippiello ◽  
Paolo Politi
Keyword(s):  
Ising Model ◽  
Long Range ◽  
Characteristic Time ◽  
Opposite Sign ◽  
Mean Field ◽  
Ising Chain ◽  
One Dimensional ◽  
Dynamical Scaling ◽  
Long Range Interactions ◽  
The One

We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance rr decaying as r^{-\alpha}r−α. For \alpha =0α=0, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with \alpha >1α>1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0<\alpha <10<α<1, we show that the system shows both features, with probability P_\alpha (N)Pα(N) of having the latter one, with the different limiting behaviours \lim _{N\to \infty}P_\alpha (N)=0limN→∞Pα(N)=0 (at fixed \alpha<1α<1) and \lim _{\alpha \to 1}P_\alpha (N)=1limα→1Pα(N)=1 (at fixed finite NN). We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time \tau _\alpha (N)\sim N^\alphaτα(N)∼Nα.

Onsager reaction field theory applied to the phase diagram of Heisenberg chain with ferromagnetic long-range interaction and antiferromagnetic nearest-neighbor interaction

2021 ◽  
Vol 35 (06) ◽  
pp. 2150080
Author(s):  
Yuan Chen ◽  
Xiuzhi Zhang ◽  
Wenan Li ◽  
Jipei Chen
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Long Range ◽  
Nearest Neighbor ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Neighbor Interaction ◽  
Range Interaction ◽  
Reaction Field ◽  
The One

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) [Formula: see text]. The ferromagnetic long-range interactions considered in this paper decay as [Formula: see text] with the distance [Formula: see text] between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of [Formula: see text] and [Formula: see text]. At finite temperatures and in the region [Formula: see text] in which [Formula: see text] is dependent of [Formula: see text], the ferromagnetic-paramagnetic phase transition survives for [Formula: see text] and no phase transition exists for [Formula: see text]. At [Formula: see text], the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for [Formula: see text]. The ground state of the system keeps ferromagnetic when [Formula: see text]. But for [Formula: see text], the system becomes antiferromagnetic at all temperatures.

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