Duality with real-space renormalization and its application to bond percolation
Disordered Systems and Neural Networks
2015-06-12 v3 Statistical Mechanics
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.
Cite
@article{arxiv.1211.1521,
title = {Duality with real-space renormalization and its application to bond percolation},
author = {Masayuki Ohzeki},
journal= {arXiv preprint arXiv:1211.1521},
year = {2015}
}
Comments
10 pages, 9 figures