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Continuing our investigation into the numerical properties of theHierarchical Reference Theory, we study the square well fluid of range lambdafrom slightly above unity up to 3.6. After briefly touching upon the corecondition and the related decoupling assumption necessary for numericalcalculations, we shed some light on the way an inappropriate choice of theboundary condition imposed at high density may adversely affect the numericalresults; we also discuss the problem of the partial differential equationbecoming stiff for close-to-critical and sub-critical temperatures. Whileagreement of the theory's predictions with simulational and purely theoreticalstudies of the square well system is generally satisfactory for lambda greaterthan about 2, the combination of stiffness and the closure chosen is found torender the critical point numerically inaccessible in the current formulationof the theory for most of the systems with narrower wells. The mechanismresponsible for some deficiencies is illuminated at least partially and allowsus to conclude that the specific difficulties encountered for square wells arenot likely to resurface for continuous potentials.

The hierarchical reference theory as applied to square well fluids of variable range