Perturbation theory with variational parameter. Inequalities and estimates for the free energy
Teoretičeskaâ i matematičeskaâ fizika, Tome 15 (1973) no. 3, pp. 407-416

Voir la notice de l'article provenant de la source Math-Net.Ru

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  - 
%0 Journal Article
%A N. A. Potapkov
%T Perturbation theory with variational parameter. Inequalities and estimates for the free energy
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1973
%P 407-416
%V 15
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1973_15_3_a12/
%G ru
%F TMF_1973_15_3_a12
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/