Perturbation theory with variational parameter. Inequalities and estimates for the free energy
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 407-416
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A perturbation theory scheme is proposed on the basis of a representation of the free energy
as a sequence $F_k(\sigma_k)$ ($\sigma_k$ is the ordering parameter). From the condition of a minimum of
$F_k(\sigma_k)$ an equation of state is obtained and a phase transition temperature $T_c^{(k)}$ is determined.
For the Heisenberg and Ising models $F_2$ is calculated ($F_1$ is the well-known molecular-field approximation) and the inequality $F_1>F_2>F$ (for the Istng model) is obtained,
which shows that $F_2$ is a better approximation than $F_1$. The temperature $T_c^{(2)}$ is also determined
for both models. The behavior of the expansion for the free energy as $T\to0$ is
investigated.
@article{TMF_1973_15_3_a12,
author = {N. A. Potapkov},
title = {Perturbation theory with variational parameter. {Inequalities} and estimates for the free energy},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {407--416},
publisher = {mathdoc},
volume = {15},
number = {3},
year = {1973},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a12/}
}
TY - JOUR AU - N. A. Potapkov TI - Perturbation theory with variational parameter. Inequalities and estimates for the free energy JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1973 SP - 407 EP - 416 VL - 15 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a12/ LA - ru ID - TMF_1973_15_3_a12 ER -
N. A. Potapkov. Perturbation theory with variational parameter. Inequalities and estimates for the free energy. Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 407-416. http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a12/