Comment on: "Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods"

TL;DR

This paper examines the critical behavior of self-assembled rigid rods on a square lattice, clarifying how different statistical ensembles influence the observed universality class of the isotropic-nematic phase transition.

Contribution

It demonstrates that the discrepancy in universality class findings is due to the choice of statistical ensemble, emphasizing the importance of ensemble effects in critical behavior analysis.

Findings

Discrepancy arises from different statistical ensembles used.

Corrections to scaling functions are necessary in the canonical ensemble.

The universality class depends on the ensemble, not just the control parameter.

Abstract

The critical behavior of self-assembled rigid rods on a square lattice was recently reinvestigated by Almarza et al. [Phys. Rev. E 82, 061117 (2010)]. Based on the Binder cumulants and the value of the critical exponent of the correlation length, the authors found that the isotropic-nematic phase transition occurring in the system is in the two-dimensional Ising universality class. This conclusion contrasts with that of a previous study [L\'opez et al., Phys. Rev. E 80, 040105 (R) (2009)] which indicates that the transition at intermediate density belongs to the q = 1 Potts universality class. Almarza et al. attributed the discrepancy to the use of the density as the control parameter by L\'opez et al. The present work shows that this suggestion is not sufficient, and that the discrepancy arises solely from the use of different statistical ensembles. Finally, the necessity of making corrections to the scaling functions in the canonical ensemble is discussed.