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

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.

18 pages, 9 figures

References in corpus (12)

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Cited by in corpus (13)

• Ground state of weakly repulsive soft-core bosons on a sphere
• Pattern formation with repulsive soft-core interactions: discrete particle dynamics and Dean-Kawasaki equation
• Freezing of soft-core bosons at zero temperature: A variational theory
• Quantum Critical Behavior of One-Dimensional Soft Bosons in the Continuum
• Crystallisation of soft matter under confinement at interfaces and in wedges
• Soft-particle lattice-gas in 1d: one- and two-component cases
• Clusterization of weakly-interacting bosons in one dimension: an analytic study at zero temperature
• Emergence of an Ising critical regime in the clustering of 1D soft matter revealed through string variables
• Ground state phase diagram of ultrasoft bosons
• Ultrasoft classical systems at zero temperature
• Classical and Quantum Gases on a Semiregular Mesh
• Static density response of one-dimensional soft bosons across the clustering transition
• Evolution of static and dynamical density correlations in a one-dimensional soft-core gas from the Tonks-Girardeau limit to a clustering fluid