Universality of 3D percolation exponents and first-order corrections to scaling for conductivity exponents

By using a fast, Nested Dissection algorithm we compare the results of finite-size scaling at pc and of “p” scaling ( ) on large cubic random resistor networks [up to 500×500×500]. The “p” scaling for conductivity of both site and bond networks leads to an exponent t=2.00(1). The finite-size scaling leads to the ratio of this conductivity exponent to the coherence length exponent ν: t/ν=2.283(3). Combining these results we estimate ν=0.876(6), in excellent agreement with a value proposed by Ballesteros et al. The first-order correctional exponent ω is found to be ω=1.0(2).