Classical Heisenberg model at zero temperature
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 134-144
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It is shown under a certain rather weak condition on the pair interaction potential: $|\Lambda|^{-1}\sum_{r,r'\in\Lambda}|u_{r,r'}|^2, that the free energy of the classical Heisenberg model in the ordered as well as disordered case in the limit $T\to0$ converges to the expression corresponding to the self-consistent field approximation. As a by-product, the free energy for the Eguchi–Kawai $U(N)$ gauge model is found for arbitrary dimension $d$ of the lattice.
@article{TMF_1989_81_1_a11,
author = {M. V. Shcherbina},
title = {Classical {Heisenberg} model at~zero temperature},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {134--144},
year = {1989},
volume = {81},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a11/}
}
M. V. Shcherbina. Classical Heisenberg model at zero temperature. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 134-144. http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a11/
[1] Pastur L. A., Scherbina M. V., TMF, 61:1 (1984), 3–16 | MR
[2] Bogolyubov N. N. (ml.), Metod issledovaniya modelnykh gamiltonianov, Nauka, M., 1974 | MR
[3] Bogolyubov N. N. (ml.), Brankov I. G., Zagrebnov V. A., Kurbatov A. M., Tonchev N. S., Metod approksimiruyuschego gamiltoniana v statisticheskoi fizike, Izd-vo BAN, Sofiya, 1981
[4] Bruinsma R., Phys. Rev., B30 (1984), 289–302 | DOI | MR
[5] Pearce P. A., Thompson G. J., Progr. Theor. Phys., 55:3 (1976), 665–671 | DOI
[6] Eguchi T., Kawai, Phys. Rev. Lett., 48:12 (1982), 1063–1066 | DOI
[7] Wilson K. G., Phys. Rev., D10:8 (1974), 2445–2459
[8] Ambjorn J., Durhuus B., Olese P., Phys. Lett., 130B:2 (1983), 93–97 | DOI | MR