Weak universality of a site-percolation model with two different sizes of particles on a square lattice

A site-percolation model with two different sizes of particles is newly introduced on a square lattice. To estimate the fractal dimension and critical exponents with high accuracy, a finite-size scaling analysis is performed with a Monte Carlo simulation. The obtained fractal dimension coincides with that of the ordinary model, while the estimated exponents β, γ, and ν are slightly different from those of the ordinary model. However, the normalized exponents β̂ = β/ν and γ̂ = γ/ν remain the same as in the ordinary model, which is a manifestation of weak universality.