INHOMOGENEOUS BOND PERCOLATION ON SQUARE, TRIANGULAR AND HEXAGONAL LATTICES

• 成果类型: Article
• 署名作者: Grimmett, Geoffrey R.; Manolescu, Ioan
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP729
• 发表日期: 2013
• 页码: 2990-3025
• 关键词: conformal-invariance; random-cluster

摘要

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.