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

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 López 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 [Phys. Rev. 176, 257 (1968)].

Figure 1

Results for the Binder cumulant of the hard square lattice model in the grand canonical ensemble for different system sizes (see the legends). The filled circle marks the critical chemical potential of the HSL model and the corresponding value of $g_4^c$ for the 2D Ising universality class (for unconstrained systems) with periodic boundary conditions.

Figure 2

Results for the Binder cumulant of the hard square lattice model in the canonical ensemble. The filled circle marks the critical density of the HSL model and the corresponding value of $g_4^c$ for the 2D Ising universality class (unconstrained systems) with periodic boundary conditions. ${\rho }_0$ is the density at maximum lattice occupancy.