Title: GINZBURG-LANDAU-WILSON HAMILTONIAN FOR A MULTI-COMPONENT CONTINUOUS SYSTEM: A MICROSCOPIC DESCRIPTION
Author(s): O.V.Patsahan (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine)

Recently we proposed the microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures. It was based on the method of collective variables (CV) with a reference system. The approach allowed us to obtain the functional of the Ginzburg-Landau-Wilson (GLW) Hamiltonian expressed in terms of the collective variables (``density'' variables). The corresponding set of collective variables included the variable connected with the order parameter. In this paper, based on the previous results, we construct the GLW Hamiltonian in the phase space of the ``field'' variables $\hat{\phi_{\vec{k}}}$ (fluctuating fields) conjugate to the ``density'' variables. We apply the obtained GLW functional to the study of both the binary symmetrical mixture and the restricted primitive model. In the former case we consider the Gaussian approximation only and show that the obtained results are the same as those found previously using the CV method. In the latter case we calculate the phase diagram taking into account the powers of $\hat{\phi_{\vec{k}}}$ higher than the second one.

Key words: phase transition, a two-component continuous system, order parameter, fluctuating field
PACS: 05.70.Fh, 05.70.Jk, 65.10.+h