• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.855-865
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• 1996

In this paper, we establish the weak convergences of processes occurring in a generalized Curie-Weiss model and its dual.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.301-313
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• 1999

In this paper we obtain similar limit theorems of the Generalized Curie - Weiss model for a new class Hamiltonian. We expressed the saddlepoint approximation by large deviation rate and then obtain the limit theorems.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.515-527
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• 1996

It has been known for mean field models that the limiting distribution reflecting the asymptotic behavior of the system is non-Gaussian at the critical state. Recently, however, Papangelow showed for the critical Curie-Weiss mean field model that there exist Gaussian structures in the asymptotic behavior of the total magnetization. We construct Gaussian structures existing in the internal fluctuation of the system for the critical case of a generalized Curie-Weiss mean field model.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.215-233
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• 1995

• Bulletin of the Korean Chemical Society
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• v.14 no.4
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• pp.485-487
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• 1993

The critical behavior of the classical D-dimensional spin model (D${\ge}$2), which is intermediate model that link up the Ising (D = 1) and the spherical model (D = ${\infty}$), is studied for the case of constant coupling interaction independent of the spin-spin distance (Curie-Weiss model). Analytical results show that the critical behavior of the present model is in quantitative agreement with the prediction of the phenomenological mean-field theory independent of D. Critical temperature is calculated to be T$_c$=k/JD. This gives a quantitative explanation of the relationship between the spin degree of freedom and the critical temperature.

• Bulletin of the Korean Chemical Society
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• v.34 no.6
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• pp.1679-1683
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• 2013

Intergrowth perovskite type complex oxides $La_{0.8}Ln_{0.2}Sr_2MnCrO_{7-{\delta}}$ (Ln=La, Nd, Gd, and Dy) have been synthesized by sol-gel method. Rietveld profile analysis shows that the phases crystallize with tetragonal unit cell in the space group I4/mmm. The unit cell parameters a and c decrease with decreasing effective ionic radius of the lanthanide ion. The magnetic studies suggest that the ferromagnetic interactions are dominant due to $Mn^{3+}$-O-$Mn^{4+}$ and $Mn^{3+}$-O-$Cr^{3+}$ double exchange interactions. Both Weiss constant (${\theta}$) and Curie temperature ($T_C$) increase with decreasing ionic radius of lanthanide ion. It was found that the transport mechanism is dominated by Mott's variable range hopping (VRH) model with an increase of Mott localization energy.