Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices

TL;DR

This study uses extensive Monte Carlo simulations to precisely determine bond percolation thresholds and analyze finite-size scaling corrections for s.c., f.c.c., and b.c.c. lattices, confirming universality of critical exponents.

Contribution

The paper provides highly accurate bond percolation thresholds and finite-size scaling corrections for three key lattice types, enhancing understanding of critical phenomena in percolation theory.

Findings

Precise critical thresholds for s.c., f.c.c., and b.c.c. lattices.

Confirmation of universal critical exponents.

Validation of finite-size scaling behavior near thresholds.

Abstract

Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide very precise values of the critical thresholds for each of the lattices: pc(s.c.) = 0.248 812 6(5), pc(f.c.c.) = 0.120 163 5(10), and pc(b.c.c.) = 0.180 287 5(10). For p close to pc, the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent $tau$ (2.189(2)), the finite-size correction exponent $omega$ (0.64(2)), and the scaling function exponent $sigma$ (0.445(1)) confirmed to be universal.