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

TL;DR

This paper critiques previous claims of a Kosterlitz-Thouless-type transition in a quasi-one-dimensional hard disk system, showing through an exact transfer matrix approach that the observed power-law decay is only a finite-size crossover, not a true phase transition.

Contribution

The authors introduce an exact transfer matrix method to analyze the system, demonstrating that the purported transition is a finite-size crossover rather than a genuine thermodynamic phase transition.

Findings

Power-law decay of positional order occurs only over finite distances.

The observed transition in previous simulations is a finite-size crossover.

No true thermodynamic phase transition exists in the system.

Abstract

Huerta et al. [Phys. Rev. Research 2, 033351 (2020)] report a power-law decay of positional order in numerical simulations of hard disks confined within hard parallel walls, which they interpret as a Kosterlitz-Thouless-type caging-uncaging transition. The proposed existence of such a transition in a quasi-one-dimensional (q1D) system, however, contradicts long-held physical expectations. To clarify if the proposed ordering persists in the thermodynamic limit, we introduce an exact transfer matrix approach to expeditiously generate equilibrium configurations for systems of arbitrary size. The power-law decay of positional order is found to extend only over finite distances. We conclude that the numerical simulation results reported are associated with a crossover, and not a proper thermodynamic phase transition.