Condensed Matter Physics, 2005, vol. 8, No. 4(44), p. 665684, English
DOI:10.5488/CMP.8.4.665
Title:
The collective variables representation of simple fluids from the
point of view of statistical field theory
Author(s):
 J.M.Caillol
(Laboratoire de Physique théorique, CNRS UMR 8627,
Bât. 210, Université de ParisSud, 91405 Orsay Cedex France)
,

 O.Patsahan
(Institute for Condensed Matter Physics of
the National Academy of Sciences of Ukraine, 1 Svientsitskii Str.,
79011 Lviv, Ukraine)
,

 I.Mryglod
(Institute for Condensed Matter Physics of
the National Academy of Sciences of Ukraine, 1 Svientsitskii Str.,
79011 Lviv, Ukraine)
,

The collective variable representation (CV) of classical
statistical systems such as, for instance, simple liquids has been
intensively developed by the Ukrainian school after seminal works
by Prof. Ihor Yukhnovskii. The basis and the structure of the CV
representation are reexamined here from the point of view of
statistical field theory and compared with another exact
statistical field representation of liquids based upon a
HubbardStratonovich transform. We derive a twoloop expansion for
the grand potential and free energy of a simple fluid in both
versions of the theory. The results obtained by the two approaches
are shown to coincide at each order of the loop expansion. The
oneloop results are identical to those obtained within the
framework of the random phase approximation of the theory of
liquids. However, at the secondloop level, new expressions for
pressure and the free energy are obtained, yielding a new type of
approximation.
Key words:
statistical field theory, loop expansion, collective
variables
PACS:
05.20.Jj, 05.70.Ce
