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

scholarly journals Modified Mean-Field Theory of One-Dimensional Spin Models with Anisotropy and Long-Range Dipolar Interactions

2020 ◽  
Vol 65 (8) ◽  
pp. 691
Author(s):  
P. J. Camp ◽  
A. O. Ivanov
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Dipole Moments ◽  
Mean Field Theory ◽  
Mean Field ◽  
Effective Field ◽  
Superparamagnetic Nanoparticles ◽  
Dipolar Interactions ◽  
Strong Anisotropy ◽  
Spin Models

The effects of interactions and anisotropy on the magnetic properties of linear chains of superparamagnetic nanoparticles are studied theoretically by mapping the problem onto spin models. With zero anisotropy, the magnetic dipole moments are free to rotate, and the system resembles a classical ferromagnetic Heisenberg model with long-range dipolar interactions. With strong anisotropy, they are constrained to align with the chain, and the system resembles the classical ferromagnetic Ising model with long-range interactions. Using a modified mean-field theory, expressions for the magnetization curve and initial magnetic susceptibility are derived from the response of a single particle subject to an effective field arising from the applied field and the interactions with the other particles. Various approximations for the effective field are tested against results from Monte Carlo simulations. It is shown that, for physically relevant interaction strengths, reliable theoretical predictions for both the zero-anisotropy and strong-anisotropy cases can be derived in a simple closed form.

Long-Range Order and Short-Range Order inPd3V: Breakdown of the Mean-Field Theory

1987 ◽  
Vol 58 (21) ◽  
pp. 2245-2248 ◽  
Author(s):  
F. Solal ◽  
R. Caudron ◽  
F. Ducastelle ◽  
A. Finel ◽  
A. Loiseau
Keyword(s):  
Field Theory ◽  
Long Range ◽  
Short Range ◽  
Short Range Order ◽  
Mean Field Theory ◽  
Mean Field ◽  
Range Order ◽  
Long Range Order ◽  
The Mean
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