Equation of state of a cell fluid model with allowance for Gaussian fluctuations of the order parameter

TL;DR

This paper develops a microscopic model for the critical behavior of a cell fluid, incorporating Gaussian fluctuations of the order parameter, and analyzes its impact on the equation of state across different temperature regimes.

Contribution

It introduces a method to include Gaussian fluctuations in the equation of state of a cell fluid model, extending validity beyond the immediate critical vicinity.

Findings

Fluctuations have negligible effect above the critical temperature.

Fluctuations become significant below the critical temperature.

The developed approach is valid over a wide range of densities and temperatures.

Abstract

The paper is devoted to the development of a microscopic description of the critical behavior of a cell fluid model with allowance for the contributions from collective variables with nonzero values of the wave vector. The mathematical description is performed in the supercritical temperature range ($T>T_c$) in the case of a modified Morse potential with additional repulsive interaction. The method, developed here for constructing the equation of state of the system by using the Gaussian distribution of the order parameter fluctuations, is valid beyond the immediate vicinity of the critical point for a wide range of density and temperature. The pressure of the system as a function of chemical potential and density is plotted for various fixed values of the relative temperature, both with and without considering the above-mentioned contributions. Compared with the results of the zero-mode approximation, the insignificant role of these contributions is indicated for temperatures $T>T_c$. At $T<T_c$, they are more significant.