The functional of the grand partition function for the investigation of the liquid-gas critical point

I.R. Yukhnovskii

Physica A: Statistical Mechanics and its Applications, 1990, vol. 168, issue 3, 999-1020

Abstract: An approach for the description of a spatially homogeneous system of interacting particles in the vicinity of the critical point is proposed. An explicit expression for the functional integral form of the partition function in the grand canonical ensemble is obtained. The functional integral is defined on a set of the collective variables (CV) {ϱk}. The variable ϱk corresponds to the density vibration mode with the wave vector k. It is shown that in the vicinity of the critical point, for all k larger than some B, the CV are distributed with the Gaussian measure density. In the long wave region, k < B, the surfaces of the cumulants consisting of the correlation functions of some reference system (the reference system is a model system of particles with repulsive pair interactions) possess wide plateaus in the vicinity of the point k = 0. It is shown that due to these two facts the homogeneous system can be put in correspondance with a certain lattice system with spacing c = πB. The problem of the calculation of the partition function can be reduced to the calculation of the functional for a three-dimensional Ising model with an external field.

Date: 1990
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/037843719090268W
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:168:y:1990:i:3:p:999-1020

DOI: 10.1016/0378-4371(90)90268-W

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 ().