Universality class of the percolation in two-dimensional lattices with distortion

Hoseung Jang, Unjong Yu

Published 2019-03-28Version 1

Mitra et al. [Phys. Rev. E 99 (2019) 012117] proposed a new percolation model that includes distortion in the square lattice and concluded that it may belong to the same universality class as the ordinary percolation. But the conclusion is questionable since their results of critical exponents are not consistent. In this paper, we reexamined the new model with high precision in the square, triangular, and honeycomb lattices by using the Newman-Ziff algorithm. Through the finite-size scaling, we obtained the percolation threshold of the infinite-size lattice and critical exponents ($\nu$ and $\beta$). Our results of the critical exponents are the same as those of the classical percolation within error bars, and the percolation in distorted lattices is confirmed to belong to the universality class of the classical percolation in two dimensions.