Geodesic
The 16-vertex model of a~ferroelectric with proton tunneling
Teoretičeskaâ i matematičeskaâ fizika, Tome 108 (1996) no. 3, pp. 411-420

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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. 
@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},
     publisher = {mathdoc},
     volume = {108},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_108_3_a4/}
}
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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/