Abstract: The possible existence of low-density and high-density fluid phase equilibria in fluids with a simple potential consisting in a combination of a square shoulder and a square well is explored by means of perturbation theory and histogram-reweighting grand canonical Monte Carlo simulation. Theory is useful as a simple and computationally inexpensive way to explore large sets of potential parameters to search for potential shapes susceptible to present multiple fluid phases, later confirmed or discarded from computer simulation. It is found that some combinations of the length and energy parameters of the potential actually give rise to such behaviour.

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