REDUCED TRANSFER MATRIX APPROACH FOR ISING MODEL

2011 ◽  
Vol 25 (21) ◽  
pp. 2895-2903 ◽  
Author(s):  
TUNCER KAYA ◽  
MURAT ARIK
Keyword(s):  
Transfer Matrix ◽  
Coupling Strength ◽  
Spontaneous Magnetization ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Critical Coupling ◽  
Transfer Matrix Approach ◽  
The Mean ◽  
2D And 3D

In this work, we present a simple approximate transfer matrix method for 2D and 3D Ising ferromagnet to calculate spontaneous magnetization of the system. The critical coupling strength Kc of 2D and 3D Ising models in reduced transfer matrix approximation is obtained quite accurately by simple improvements over the mean field theory. The important physical effect we include is the some of the fluctuations effects of the systems directly with help of this method. We predict from the spontaneous magnetization curve that the critical coupling strength Kc=J/kBT = 0.401 and 0.245 for two-dimensional (2D) and three-dimensional (3D) systems, respectively.

MEAN-FIELD THEORY FOR LAYERED HIGH-TEMPERATURE SUPERCONDUCTORS

1988 ◽  
Vol 02 (05) ◽  
pp. 1059-1065 ◽  
Author(s):  
D. Baeriswyl ◽  
T. Schneider
Keyword(s):  
High Temperature Superconductors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
Interlayer Spacing ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pairing Mechanism ◽  
The Mean

Using the mean-field approximation we study a model for quasi-two-dimensional layered superconductors. The interlayer coupling, assumed to be mediated by a small electron hopping term, is found to leave Tc practically unaffected. Consequently, a three-dimensional pairing mechanism is required to explain the observed dependence of Tc on the average interlayer spacing in the Bi and Tl compounds.

Spin glasses: recent advances in mean-field theory

1987 ◽  
Vol 65 (10) ◽  
pp. 1245-1250 ◽  
Author(s):  
B. W. Southern
Keyword(s):  
Field Theory ◽  
Spin Glasses ◽  
Glass Phase ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Spin Glass Phase ◽  
Ising Spin ◽  
Recent Advances ◽  
The Mean

A survey of recent advances in the mean-field theory of Ising spin glasses is presented. The physical picture of the spin-glass phase predicted by this theory is described, and its relationship to real three-dimensional systems is discussed.

IMPROVED MEAN-FIELD TRANSFER MATRIX MODEL FOR HYPERCUBIC ISING SYSTEMS

2012 ◽  
Vol 26 (17) ◽  
pp. 1250111 ◽  
Author(s):  
TUNCER KAYA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Transfer Matrix ◽  
Coupling Strength ◽  
Mean Field ◽  
Field Method ◽  
Critical Coupling ◽  
Average Magnetization ◽  
Self Consistent ◽  
Ising Systems

A mean-field method for Ising systems is introduced generalizing the reduced transfer matrix method introduced by Kaya and Arık. The important assumption of the method is that the neighboring spins of a central spin can be replaced by the average magnetization 〈σ〉 of the system. The approximation is same as the previously introduced method. However, the derivative of average magnetization with respect to external magnetic field is defined without further approximation. In addition, the previously introduced model is extended to all hypercubic lattices. The critical coupling strength Kc for hypercubic lattices is evaluated self-consistently. Obviously, this assumption leads to some significant deviation from the exact treatment. However, the model introduced here is an improvement on most self-consistent mean-field-type approximations.

scholarly journals Evidence of exactness of the mean-field theory in the nonextensive regime of long-range classical spin models

2000 ◽  
Vol 61 (17) ◽  
pp. 11521-11528 ◽  
Author(s):  
Sergio A. Cannas ◽  
A. C. N. de Magalhães ◽  
Francisco A. Tamarit
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Mean Field Theory ◽  
Mean Field ◽  
Spin Models ◽  
Classical Spin ◽  
The Mean ◽  
Classical Spin Models
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