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 (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.
Highlights
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]
The proposal is intriguing because the presence of a phase transition in such a system is physically unexpected
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 that the KT-like scaling observed in numerical simulations results from a smooth crossover rather than a genuine thermodynamic phase transition
Summary
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]. (Singularities with respect to changes in structural quantities remain possible [5].) KT transitions, differ from conventional phase transitions in many respects [6,7] They leave no thermal feature in the partition function and its derivatives, such as the specific heat [8], and are “infinite order” in nature. That critical phase is only identified from the power-law decay of spatial correlations, with a critical exponent value that changes with system conditions [7]. Do these features exempt KT transitions from traditional expectations for q1D systems? Do these features exempt KT transitions from traditional expectations for q1D systems? If not, how can one explain the power-law decay of the positional order observed in the simulations of Ref. [1]?
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
