Reply to Comment on Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods

TL;DR

This paper discusses the nature of the phase transition in a model of polydisperse rigid rods on a lattice, contrasting different ensemble results and theoretical predictions about criticality and renormalization.

Contribution

It clarifies the discrepancy between observed critical behaviors in different ensembles and theoretical expectations for the model.

Findings

Different ensembles show contrasting critical behaviors.

The model exhibits Ising criticality in the grand canonical ensemble.

No renormalization of exponents occurs for constrained systems with specific heat anomalies.

Abstract

We comment on the nature of the ordering transition of a model of equilibrium polydisperse rigid rods, on the square lattice, which is reported by Lopez et al. to exhibit random percolation criticality in the canonical ensemble, in sharp contrast to (i) our results of Ising criticality for the same model in the grand canonical ensemble [Phys. Rev. E 82, 061117 (2010)] and (ii) the absence of exponent(s) renormalization for constrained systems with logarithmic specific heat anomalies predicted on very general grounds by Fisher [M.E. Fisher, Phys. Rev. 176, 257 (1968)].