Absence of criticality in the hypernetted chain equation for a truncated potential

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Abstract
The three-dimensional HNC equation for a truncated Lennard-Jones potential is numerically solved. We have found that the direct correlation function asymptotically behaves as r -2 exp (-2r/ξ), ξ being the correlation length. The contribution coming from this behaviour has been incorporated into the computation of the isothermal compressibility κT. The results seem to indicate that the HNC equation does not have real solutions inside a certain region in the temperature-density plane, whose boundary line has been fitted to power laws. When approaching this boundary, κT and ξ tend to finite values. So, a true critical point, where κT and ξ would diverge, is not present.