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