Inhomogeneous bond percolation on square, triangular and hexagonal lattices

Abstract

The star-triangle transformation is used to obtain an equivalence extending over the set of all (in)homogeneous bond percolation models on the square, triangular and hexagonal lattices. Among the consequences are box-crossing (RSW) inequalities for such models with parameter-values at which the transformation is valid. This is a step toward proving the universality and conformality of these processes. It implies criticality of such values, thereby providing a new proof of the critical point of inhomogeneous systems. The proofs extend to certain isoradial models to which previous methods do not apply.

Published in at http://dx.doi.org/10.1214/11-AOP729 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• An introduction to the dimer model
• Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
• Universality for bond percolation in two dimensions

Cited by in corpus (9)

• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Bond percolation on isoradial graphs: criticality and universality
• Universality for bond percolation in two dimensions
• Universality for the random-cluster model on isoradial graphs
• Percolation since Saint-Flour
• Dimers and analytic torsion I
• Rotational invariance in critical planar lattice models
• Rigorous Confidence Intervals on Critical Thresholds in 3 Dimensions
• Structure of Gibbs measures for planar FK-percolation and Potts models