Higher orders of self-similar approximations for thermodynamic potentials

V.I. Yukalov and E.P. Yukalova

Physica A: Statistical Mechanics and its Applications, 1994, vol. 206, issue 3, 553-580

Abstract: The problem of calculating thermodynamic potentials in statistical mechanics by using the method of self-similar approximations developed by the authors is considered. An emphasis is made on the search for a regular procedure of defining higher-order terms providing a good accuracy and stability of the method. It is shown how the renormalized perturbation theory can be reformulated to the language of dynamical theory. Then, instead of sequences of approximants one can study trajectories of cascades whose fixed-point attractors play the role of the limits for the corresponding sequences of perturbative terms. As an illustration of the procedure the free energy of a zero-dimensional ϕ4 model is calculated up to the third order of the self-similar approximation whose precision is found to be greater than 0.1% for all coupling parameters ranging from zero to infinity.

Date: 1994
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0378437194903247
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:206:y:1994:i:3:p:553-580

DOI: 10.1016/0378-4371(94)90324-7

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().