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

TL;DR

This paper proves that one-dimensional Penetrable Square Wells do not exhibit phase transitions, extending the understanding of phase behavior in ultra-soft colloid models and related fluids.

Contribution

It provides a rigorous proof of the absence of phase transitions in this model using the Kastner, Schreiber, and Schnetz theorem, complementing van Hove's theorem.

Findings

No phase transition occurs in one-dimensional Penetrable Square Wells.

The proof applies to a broad class of model fluids.

Supports the theoretical understanding of phase behavior in ultra-soft colloids.

Abstract

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.