Duality with real-space renormalization and its application to bond percolation

Abstract

We obtain the exact solution of the bond-percolation thresholds with inhomogenous 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 compared to the very recent study on the same problem [R. M. Ziff, et. al., J. Phys. A: Math. Theor. 45 (2012) 494005]. The resultant generic formulas from our derivation can give several estimations for the bond-percolation thresholds on other lattices rather than the square lattice.

10 pages, 9 figures

References in corpus (7)

• Locations of multicritical points for spin glasses on regular lattices
• Multicritical points for the spin glass models on hierarchical lattices
• Critical surfaces for general bond percolation problems
• Critical manifold of the kagome-lattice Potts model
• The critical manifolds of inhomogeneous bond percolation on bow-tie and checkerboard lattices
• The percolation critical polynomial as a graph invariant
• Duality analysis on random planar lattice

Cited by in corpus (5)

• Percolation on complex networks: Theory and application
• High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials
• Thermodynamic Comparison and the Ideal Glass Transition of A Monatomic Systems Modeled as an Antiferromagnetic Ising Model on Husimi and Cubic Recursive Lattices of the Same Coordination Number
• An extension of estimation of critical points in ground state for random spin systems
• A simple relation between frustration and transition points in diluted spin glasses