Geodesic
The 16-vertex model of a ferroelectric with proton tunneling
Teoretičeskaâ i matematičeskaâ fizika, Tome 108 (1996) no. 3, pp. 411-420 
V. N. Likhachev; V. A. Onischuk; A. Rosenhren. The 16-vertex model of a ferroelectric with proton tunneling. Teoretičeskaâ i matematičeskaâ fizika, Tome 108 (1996) no. 3, pp. 411-420. http://geodesic.mathdoc.fr/item/TMF_1996_108_3_a4/
@article{TMF_1996_108_3_a4,
     author = {V. N. Likhachev and V. A. Onischuk and A. Rosenhren},
     title = {The 16-vertex model of a~ferroelectric with proton tunneling},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {411--420},
     year = {1996},
     volume = {108},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_108_3_a4/}
}
TY  - JOUR
AU  - V. N. Likhachev
AU  - V. A. Onischuk
AU  - A. Rosenhren
TI  - The 16-vertex model of a ferroelectric with proton tunneling
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 411
EP  - 420
VL  - 108
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_108_3_a4/
LA  - ru
ID  - TMF_1996_108_3_a4
ER  - 
%0 Journal Article
%A V. N. Likhachev
%A V. A. Onischuk
%A A. Rosenhren
%T The 16-vertex model of a ferroelectric with proton tunneling
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 411-420
%V 108
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1996_108_3_a4/
%G ru
%F TMF_1996_108_3_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

Thermodynamics of the 1D ferroelectric model with proton tunneling has been reduced to the calculation of the grand partition function of the 1D Ising model of spin $S=1$ in the transverse field $\Gamma$. This allows the behaviour of the initial model to be calculated in the vicinity of its thermodynamic anomaly. In the second order, the dependence of the free energy on temperature, and the tunneling parameter $\Gamma$ was found.

[1] M. E. Lines, A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials, Clarendon Press, Oxford, 1977

[2] Y. Morimoto, Y. Tokura, N. Nagaosa, T. Suzuki, Phys. Rev. Lett., 71 (1993), 2833 | DOI

[3] L. Pauling, J. Am. Chem. Soc., 57 (1938), 2680 ; J. C. Slater, J. Chem. Phys., 9 (1941), 16 | DOI | DOI

[4] V. E. Zubkus, V. A. Onischuk, E. E. Tornau, A. Rosengren, Phys. Rev., B49 (1994), 3774 | DOI

[5] J. F. Nagle, Am. J. Phys., 36 (1968), 1114 ; S. R. Salinas, J. F. Nagle, Phys. Rev., B9 (1974), 4920 | DOI | DOI

[6] L. N. Bulaevskii, ZhETF, 51 (1966), 230; Sov. Phys. JETP, 24 (1967), 154

[7] A. A. Abricosov, L. P. Gorkov, I. E. Dsialoshinsky, Methods of Quantum Field Theory in Statistical Physics, Moscow, 1962

[8] H. Araki, Comm. Math. Phys., 14 (1969), 120 | DOI | MR | Zbl

[9] A. Gurvitz, Vorlesungen über allgemeine Funktionen Theorie und elliptische Funktionen, Springer, 1964 | MR

[10] R. J. Bakster, Exactly Solved Models in Statistical Mechanics, ch. 2, Acad. Press, London–New York, 1982 | MR

[11] D. Ruelle, Statistical Mechanics. Rigorous Results, ch. 2, W. A. Benjamin Inc., New York–Amsterdam, 1969 | MR | Zbl