title: Duality with real-space renormalization and its application to bond percolation.
abstract: We obtain the exact solution of the bond-percolation thresholds with inhomogeneous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in the spin-glass theory. Our formulation is a more straightforward way than that of a very recent study on the same problem [R. M. Ziff et al., J. Phys. A: Math. Theor. 45, 494005 (2012)]. The resultant generic formulas from our derivation can give several estimations for the bond-percolation thresholds on other lattices rather than the square lattice.
authors: Department of Systems Science, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Kyoto 606-8501, Japan.
authors: Masayuki
authors: M
authors: Ohzeki
mesh_terms: D003198:Computer Simulation; D005898:Glass / Q000737:chemistry*; D008956:Models, Chemical; D008958:Models, Molecular; D015233:Models, Statistical; D044367:Phase Transition