Perturbation theory with variational parameter. Inequalities and estimates for the free energy
Unknown
Submitted 1973 | SovietRxiv: ru-197301.18482 | Original in English | Abstract Only

Abstract

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.

Submission history

Perturbation theory with variational parameter. Inequalities and estimates for the free energy