Effective magnetic Hamiltonian and Ginzburg criterion for fluids

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Abstract
We develop further the approach of Hubbard and Schofield [Phys. Lett. 40A, 245 (1972)], which maps the fluid Hamiltonian onto a magnetic one. We show that all coefficients of the resulting effective Landau-Ginzburg-Wilson (LGW) Hamiltonian may be expressed in terms of the compressibility of a reference fluid containing only repulsive interactions and its density derivatives; we calculate the first few coefficients in the case of the hard-core reference fluid. From this LGW Hamiltonian we deduce approximate mean-field relations between critical parameters and test them on data for Lennard-Jones, square-well, and hard-core Yukawa fluids. We estimate the Ginzburg criterion for these fluids.
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