Effective Magnetic Hamiltonian and Ginzburg Criterion for Fluids

TL;DR

This paper develops a method to derive an effective magnetic Hamiltonian for fluids, expressing its coefficients through the fluid's compressibility, and tests the resulting critical relations on various fluid models.

Contribution

It introduces a way to relate the fluid Hamiltonian to a magnetic one using compressibility, providing a new approach to analyze fluid critical phenomena.

Findings

Derived coefficients of the LGW Hamiltonian from reference fluid properties.

Established mean-field relations for critical parameters.

Estimated the Ginzburg criterion for different fluid models.

Abstract

We develop further the approach of Hubbard and Schofield (Phys.Lett., A40 (1972) 245), 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.