Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system

Abstract

The simplicity of a quasi-one-dimensional system of hard disks enables us to get a much deeper and more quantitative insight into the solid-to-fluid transformation and identify it as caging-uncaging transition. Both computer simulation data and theoretical results show that density decrease induces progressively larger number of uncaged disk pairs which exchange their transverse positions through windows in the initial crystalline zigzag array. At low densities windows dominate and disks are moving independently (pairs "dissociate"). Along with the simulation data on the transversal excitation modes and pair correlation function this shows that the solid-toliquid transformation is a continuous Kosterlitz-Thouless-type transition.

Comment on "Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system" [Phys. Rev. Research 2, 033351 (2020)]

“…At long distances, however, while Ref. [1] reports that g(x)−1 decays with a characteristic power-law beyond a certain density, we find that for sufficiently large x, g(x) − 1 decays exponentially for all densities considered. For ρ = 1.1111, in particular, we observe that the power-law-like decay terminates at x ∼ 100, even though it persists at least up to x ∼ 200 in simulations.…”

“…By broadening the range of g(x) compared to what Ref. [1] reports, we find that its power-law decay is truncated at large distances, and hence that the KT-like scaling observed in numerical simulations results from a smooth crossover rather than a genuine thermodynamic phase transition.…”

“…(Although this scheme differs from the canonical, constant N V T ensemble simulated in Ref. [1], in the thermodynamic limit the two are rigorously equivalent.) An entry of the transfer matrix then reads…”

“…The work of Huerta et al identifies a Kosterlitz-Thouless (KT)-type caging-uncaging transition in a system of hard disks confined between parallel walls [1]. That identification is based on the power-law decay of positional order in numerical simulations near close packing, and is supported by the detection of a narrow subpeak in the pair distribution function and of transverse excitation modes in the caging and uncaging regimes.…”

“…If not, how can one explain the power-law decay of the positional order observed in the simulations of Ref. [1]?…”