Phase diagrams of random spin systems. II. Bethe approximation

1980 ◽  
Vol 13 (26) ◽  
pp. 5059-5070 ◽  
Author(s):  
S Sarbach
Keyword(s):  
Phase Diagrams ◽  
Spin Systems ◽  
Bethe Approximation

CONTROLLED RANDOMNESS AND FRUSTRATION OF THE MANY-BODY INTERACTIONS

2011 ◽  
Vol 25 (26) ◽  
pp. 3529-3538 ◽  
Author(s):  
YOICHIRO HASHIZUME ◽  
MASUO SUZUKI
Keyword(s):  
Spin Glass ◽  
Phase Diagrams ◽  
Glass Phase ◽  
Spin Systems ◽  
Ferromagnetic Phase ◽  
Glass Transitions ◽  
Many Body ◽  
Spin Pair ◽  
Ising Spin ◽  
Many Body Interactions

On the Ising spin systems constructed with four-body interactions, there appears the "spin-pair ordered phase" or "spin-pair glass phase" in a certain temperature. Especially, the random four-body models include the frustration and the spin-pair glass phase appears in those models. This frustration may play an important role of spin-pair glass transitions, similarly to the case of ordinary spin-glass transitions. In this study, we clarify the way to discriminate quantitatively "frustrated unit cells" from "nonfrustrated ones" on the random four-body models. Then we introduce a parameter to control the frustration in the Ising spin systems with random four-body interactions. This parameter enables us to analyze the frustration continuously in many-body models. Thus we have analyzed the phase transitions and obtained phase diagrams using the frustration parameter. These interesting phase diagrams show that there appear the spin-pair ordered phases even on the completely frustrated models. This result is essentially different from the random two-body models, namely spin-glass models (there appears no ferromagnetic phase in the fully frustrated spin-glass models, which correspond to the Villain models).

Phase diagrams for two-dimensional six- and eight-states spin systems

1985 ◽  
Vol 18 (1) ◽  
pp. 73-82 ◽  
Author(s):  
R Badke ◽  
P Reinicke ◽  
V Rittenberg
Keyword(s):  
Phase Diagrams ◽  
Spin Systems ◽  
Two Dimensional

COHERENT-ANOMALY METHOD FOR QUANTUM SPIN SYSTEMS

1988 ◽  
Vol 02 (01) ◽  
pp. 1-11 ◽  
Author(s):  
NOBUYASU ITO ◽  
MASUO SUZUKI
Keyword(s):  
Critical Exponents ◽  
Heisenberg Model ◽  
Spontaneous Magnetization ◽  
Quantum Spin ◽  
Spin Systems ◽  
Quantum Spin Systems ◽  
Cubic Lattice ◽  
Bethe Approximation ◽  
Simple Cubic ◽  
Simple Cubic Lattice

The coherent-anomaly method (CAM) is applied to the Heisenberg model to test the applicability of the CAM for quantum spin systems. The Weiss, Bethe and constant coupling approximations are tried for the Heisenberg model on the simple cubic lattice and estimate the critical exponents of the susceptibility and spontaneous magnetization using the CAM. The results show that the CAM is also powerful for quantum spin systems. The detailed results of the Bethe approximation of the spin-1/2 isotropic Heisenberg model are presented.

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