Weak Universality of a Site-Percolation Model with Two Different Sizes of Particles on a Square Lattice.

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  • Sahara Ryoji
    Institute for Materials Research, Tohoku University, Sendai 980–8577
  • Mizuseki Hiroshi
    Institute for Materials Research, Tohoku University, Sendai 980–8577
  • Ohno Kaoru
    Institute for Materials Research, Tohoku University, Sendai 980–8577
  • Kawazoe Yoshiyuki
    Institute for Materials Research, Tohoku University, Sendai 980–8577

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Abstract

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 hat β = β / ν and hat γ = γ / ν remain the same as in the ordinary model, which is a manifestation of weak universality.

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