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.

SHORT-TIME DYNAMICS OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

2003 ◽  
Vol 17 (23) ◽  
pp. 1227-1236 ◽  
Author(s):  
YUAN CHEN ◽  
ZHI-BING LI
Keyword(s):  
Long Range ◽  
High Temperature Phase ◽  
Vector Model ◽  
Temperature Phase ◽  
Range Interaction ◽  
Time Dynamics ◽  
Long Range Interaction ◽  
Renormalization Group Approach ◽  
Short Time ◽  
N Vector

The short-time critical behavior of the random n-vector model with long-range interaction is studied by the theoretic renormalization-group approach. After a sudden quench to the critical temperature from the high temperature phase, the system is released to an evolution within model A dynamics. The initial slip exponents and the dynamic exponent are calculated to two-loop order.

scholarly journals Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

2019 ◽  
Vol 21 (11) ◽  
pp. 6216-6223 ◽  
Author(s):  
Daniel Silva ◽  
Per Arne Rikvold
Keyword(s):  
Phase Diagrams ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Square Lattice ◽  
Temperature Phase ◽  
Zero Temperature ◽  
Dimensional Parameter ◽  
State Diagrams ◽  
Solid Foundation

The fifteen topologically different zero-temperature phase diagrams in the model's full, five-dimensional parameter space provide a solid foundation for studies at finite temperatures.

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.

DAMAGE SPREADING ON THE HOMO- AND HETERO-CELL LATTICES WITH COMPETING GLAUBER AND KAWASAKI DYNAMICS

2008 ◽  
Vol 22 (16) ◽  
pp. 2545-2555 ◽  
Author(s):  
Z. Z. GUO ◽  
XIAO-WEI WU
Keyword(s):  
Long Range ◽  
Nearest Neighbor ◽  
Hexagonal Lattice ◽  
Interaction Strength ◽  
Spin Interaction ◽  
Kawasaki Dynamics ◽  
Range Interaction ◽  
Damage Spreading ◽  
Spin Interactions ◽  
Long Range Interaction

The damage spreading of the Ising model on the homo- and hetero-cell lattices (here the topological hexagonal lattice and the 4–8 lattice) with competing Glauber (G-) and Kawasaki (K-) dynamics is studied and the results are compared. For the homo-cell lattice, we pay attention to the pure K-dynamics or the cases in which the K-dynamics is dominant. We get four main conclusions related to the K-dynamics through our calculations: (1) the damage always spreads as long as Kawasaki dynamics is dominant during the competition of two dynamics; (2) the relation for the saturation damage, 〈s〉∞ = 0.5, holds for K-dynamics whatever the updating rules are; (3) 〈s〉∞ = 0.5 is independent of the structures of the system; (4) the DS process under pure K-dynamics converges very slowly, especially for T = 0 K-dynamics. For the hetero-cell lattice, we are interested in the long-range interaction between spins and the different interaction strength for the spins in the hetero-cells. To include the long-range spin interaction, we consider the spin interactions up to next-nearest neighbors. It is shown that the inclusion of the next-nearest-neighbor interaction enhances the transition temperature greatly. The explanation and discussion for the results are presented.

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