We study the orientational ordering on the surface of a sphere using Monte Carlo and Brownian dynamics simulations of rods interacting with an anisotropic potential. We restrict the orientations to the local tangent plane of the spherical surface and fix the position of each rod to be at a discrete point on the spherical surface. On the surface of a sphere, orientational ordering cannot be perfectly nematic due to the inevitable presence of defects. We find that the ground state of four +1/2 point defects is stable across a broad range of temperatures. We investigate the transition from disordered to ordered phase by decreasing the temperature and find a very smooth transition. We use fluctuations of the local directors to estimate the Frank elastic constant on the surface of a sphere and compare it to the planar case. We observe subdiffusive behavior in the mean square displacement of the defect cores and estimate their diffusion constants.
In Romano's Comment [Phys. Rev. E 91, 046501 (2015)] on Sec. II of our paper [Phys. Rev. E 90, 022502 (2014)], the author suggests that our findings concerning the nature of the ordering transition of our modified Lebwohl-Lasher model with two-dimensional planar rotators on a planar lattice are inconsistent with known mathematical results. We argue in this Reply that our findings are in fact in agreement with previous mathematical and simulation results and that the criticisms raised by Romano have no impact on the results presented in our paper.
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