Perturbation theory in systems with long-range potential
Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 3, pp. 410-414
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A one-dimensional model with interaction energy $E=-I\sum_{i\not=j} e^{-\gamma(|i-j|-1)} \mu_i \mu_j$ of a definite configuration of spins is considered. A perturbation theory for large $\gamma$ is developed, the zeroth approximation being the model with only nearest-neighbor interaction. It is shown that at large $\gamma$ the free energy can be represented by a series in powers of $e^{-\gamma}$. The values of $\gamma$ for which this expansion is valid are found. The possibility of applying the method to two- and three-dimensional systems is considered.
@article{TMF_1982_50_3_a10,
author = {G. V. Klimachev},
title = {Perturbation theory in systems with long-range potential},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {410--414},
year = {1982},
volume = {50},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1982_50_3_a10/}
}
G. V. Klimachev. Perturbation theory in systems with long-range potential. Teoretičeskaâ i matematičeskaâ fizika, Tome 50 (1982) no. 3, pp. 410-414. http://geodesic.mathdoc.fr/item/TMF_1982_50_3_a10/