Comment on "kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system"

Abstract

Huerta [Phys. Rev. Research 2, 033351 (2020)2643-156410.1103/PhysRevResearch.2.033351] 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 (KT)-type caging-uncaging transition. The proposed existence of such a transition in a quasi-one-dimensional 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 configurations of very large subsystems that are typical of equilibrium thermodynamic (infinite-size) systems. 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 unrelated to KT-type physics, and not with a proper thermodynamic phase transition.