The equation of state of a cell fluid model in the supercritical region

TL;DR

This paper develops an analytic method using renormalization group techniques to derive the equation of state for a cell fluid model in the supercritical region, accounting for non-Gaussian fluctuations near the critical point.

Contribution

It introduces a novel analytical approach to calculate the equation of state and critical temperature of a fluid model above the critical point, incorporating non-Gaussian fluctuations.

Findings

Derived the equation of state in the supercritical region.

Calculated the critical temperature of the fluid model.

Plotted isothermal compressibility as a function of density.

Abstract

The analytic method for deriving the equation of state of a cell fluid model in the region above the critical temperature ($T \geqslant T_\text{c}$) is elaborated using the renormalization group transformation in the collective variables set. Mathematical description with allowance for non-Gaussian fluctuations of the order parameter is performed in the vicinity of the critical point on the basis of the $\rho^4$ model. The proposed method of calculation of the grand partition function allows one to obtain the equation for the critical temperature of the fluid model in addition to universal quantities such as critical exponents of the correlation length. The isothermal compressibility is plotted as a function of density. The line of extrema of the compressibility in the supercritical region is also represented.