Non existence of a phase transition for the Penetrable Square Wells in one dimension

Penetrable Square Wells in one dimension were introduced for the first time in [A. Santos et. al., Phys. Rev. E, 77, 051206 (2008)] as a paradigm for ultra-soft colloids. Using the Kastner, Schreiber, and Schnetz theorem [M. Kastner, Rev. Mod. Phys., 80, 167 (2008)] we give strong evidence for the absence of any phase transition for this model. The argument can be generalized to a large class of model fluids and complements the van Hove’s theorem.