We can determine the phase transition boundaries according to the definition of these phase categories: either the entire transition zone or its upper limit, which lies between homogeneous fluids and the coexistence phase. We emphasize that the goal in this case is just broadly determining a region for the boundaries, not obtaining accurately the conditions of the phase transition. Upon comparing the transition regions of the HhPF and the MGCM results, it is noticeable that the phase boundary in the HhPF is moved to lower temperatures. This reduction in transition temperature is attributed to the shallower potential in HhPF, as previously discussed and illustrated in Figure . Note that the phase transition boundary for HhPF is more aligned with that of the Lennard-Jones potential, both in shape and in critical temperatures. In contrast, the transition boundary for MGCM is significantly higher than that of Lennard-Jones, because of the broader potential of MGCM, which leads to stronger interactions over longer distances following the first RDF peak.