Work

Inhomogeneous bond percolation on square, triangular and hexagonal lattices

Year: 2013

Type: article

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.

Source: The Annals of Probability

DOI: 10.1214/11-aop729

Authors: Geoffrey R. Grimmett, Ioan Manolescu

Institution: University of Cambridge

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Cambridge, Engineering and Physical Sciences Research Council

Awards: G8324530333, G8842255166