Probing the existence of phase transitions in one-dimensional fluids of penetrable particles

TL;DR

This paper investigates whether phase transitions occur in one-dimensional fluids of penetrable particles, specifically the GEM-4 model, and concludes that what appears as transitions are likely just sharp crossovers based on multiple theoretical approaches.

Contribution

The study applies three different theoretical methods to analyze the one-dimensional GEM-4 model, providing evidence that observed transitions are probably crossovers rather than true phase transitions.

Findings

Evidence suggests no true phase transitions, only sharp crossovers.

Multiple theoretical approaches agree on the crossover nature.

Supports previous simulation results indicating the absence of genuine phase transitions.

Abstract

Phase transitions in one-dimensional classical fluids are usually ruled out by making appeal to van Hove's theorem. A way to circumvent the conclusions of the theorem is to consider an interparticle potential that is everywhere bounded. Such is the case of, {\it e.g.}, the generalized exponential model of index 4 (GEM-4 potential), which in three dimensions gives a reasonable description of the effective repulsion between flexible dendrimers in a solution. An extensive Monte Carlo simulation of the one-dimensional GEM-4 model [S. Prestipino, {\em Phys. Rev. E} {\bf 90}, 042306 (2014)] has recently provided evidence of an infinite sequence of low-temperature cluster phases, however also suggesting that upon pushing the simulation forward what seemed a true transition may eventually prove to be only a sharp crossover. We hereby investigate this problem theoretically, by three different and increasingly sophisticated approaches ({\it i.e.}, a mean-field theory, the transfer matrix of a lattice model of clusters, and the exact treatment of a system of point clusters in the continuum), to conclude that the alleged transitions of the one-dimensional GEM4 system are likely just crossovers.