Possible manifestation of nonuniversality in some continuum percolation systems

Using Monte Carlo and finite element simulations, we analyse the critical exponents s and t governing the behaviour of the real, epsilon', and imaginary, epsilon '', parts of the effective permittivity of two-phase random heterostructures near the percolation threshold phi(2c). Specifically, we report on a systematic study of the critical behaviour of statistically isotropic distributions of penetrable discs of radius R (or random arrays of parallel, infinitely long, identical, partially penetrable circular cylinders) randomly placed in a unit square subject to periodic boundary conditions. Interestingly, we find that the radial distribution function shows great sensitivity to the degree of impenetrability. of the discs. The present data set indicates that s > t for a given value of. and that 1.34 <= s <= 1.54 and 0.70 <= t <= 1.11, in contrast to the universal values (s = t = 1.3) for two-dimensional continuum percolation systems. One might speculate that this value of t is a signature of finite-size effects. However, a finite-size analysis carried out by considering systems of increasing size, i.e. 0.03 <= R <= 0.1, at each., indicates that there is no appreciable change in t over the range of R explored. As the distance to f2c is decreased, epsilon' and epsilon '' display a smooth transition from a power-law dependence, which is well fitted by the standard percolation expression, to a plateau regime. We associate the plateau with finite-size effects and the short-range multipolar interactions localized in disc clusters.