Geodesic
Integration of the stationary problem for a classical spin chain
Teoretičeskaâ i matematičeskaâ fizika, Tome 71 (1987) no. 1, pp. 154-159 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A general solution of the stationary problem for anisotropic discrete Heisenberg lattice with classical spins and its natural generalization, the discrete version of the classical $n$-dimensional Neumann problem is found. Explicit formulas for solutions in terms of the $\theta$-functions and expressions for energies of these solutions are obtained. Integration is based on the interpretation of the solution in terms of the Bloch eigenfunction of the discrete Schrödinger operator. 
@article{TMF_1987_71_1_a14,
     author = {A. P. Veselov},
     title = {Integration of the stationary problem for a~classical spin chain},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {154--159},
     year = {1987},
     volume = {71},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a14/}
}
TY  - JOUR
AU  - A. P. Veselov
TI  - Integration of the stationary problem for a classical spin chain
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1987
SP  - 154
EP  - 159
VL  - 71
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a14/
LA  - ru
ID  - TMF_1987_71_1_a14
ER  - 
%0 Journal Article
%A A. P. Veselov
%T Integration of the stationary problem for a classical spin chain
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1987
%P 154-159
%V 71
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a14/
%G ru
%F TMF_1987_71_1_a14
A. P. Veselov. Integration of the stationary problem for a classical spin chain. Teoretičeskaâ i matematičeskaâ fizika, Tome 71 (1987) no. 1, pp. 154-159. http://geodesic.mathdoc.fr/item/TMF_1987_71_1_a14/

[1] Belobrov P. I., Beloshapkin V. V., Zaslavskii G. M., Tretyakov A. G., ZhETF, 87:1 (1984), 310–322

[2] Granovskii Ya. G., Zhedanov A. S., ZhETF, 89:6 (1985), 2156–2163

[3] Granovskii Ya. G., Zhedanov A. S., TMF, 71:1 (1987), 143–153 | MR

[4] Pokrovskii V. L., Khokhlachev S. B., Pisma v ZhETF, 22:7 (1975), 371 –373

[5] Mozer Yu., UMN, 36:5 (1981), 109–151 | MR | Zbl

[6] Veselov A. P., Funkts. analiz i ego prilozh., 14:1 (1980), 48–50 | MR | Zbl

[7] Dubrovin B. A., Matveev V. B., Novikov S. P., UMN, 31:1 (1976), 55–136 | MR | Zbl

[8] Dubrovin B. A., Krichever I. M., Novikov S. P., “Integriruemye sistemy, I”, Sovremennye problemy matematiki. Fundamentalnye napravleniya, 4, VINITI, M., 1985, 179–277 | MR | Zbl

[9] Brazovskii S. A., Dzyaloshinskii I. E., Krichever I. M., ZhETF, 83:1 (1982), 389–415 | MR

[10] Veselov A. P., Novikov S. P., DAN SSSR, 279:1 (1984), 20–24 | MR | Zbl