True Widom line for a square-well system

In the present paper we propose a van der Waals-like model that allows a purely analytical study of fluid properties including the equation of state, phase behavior, and supercritical fluctuations. We take a square-well system as an example and calculate its liquid-gas transition line and supercritical fluctuations. Employing this model allows us to calculate not only the thermodynamic response functions (isothermal compressibility βT, isobaric heat capacity CP, density fluctuations ζT, and thermal expansion coefficient αT), but also the correlation length in the fluid ξ. It is shown that the bunch of extrema widens rapidly upon departure from the critical point. It seems that the Widom line defined in this way cannot be considered as a real boundary that divides the supercritical region into gaslike and liquidlike regions. As it has been shown recently, a dynamic line on the phase diagram in the supercritical region, namely, the Frenkel line, can be used for this purpose.