Bond percolation on isoradial graphs: criticality and universality

DOI10.1007/s00440-013-0507-yzbMath1296.60263arXiv1204.0505OpenAlexW2108994572MaRDI QIDQ2249588

Ioan Manolescu, Geoffrey R. Grimmett

Publication date: 2 July 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0505

zbMATH Keywords

bond percolationrhombic tilinginhomogeneous percolationPenrose tilingisoradial graph

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items

On the critical parameters of theq≤ 4 random-cluster model on isoradial graphs, Martin boundary of killed random walks on isoradial graphs, Universality for bond percolation in two dimensions, A Biography of Robert M Ziff, Isoradial immersions, Cube moves for \(s\)-embeddings and \(\alpha\)-realizations, An upper bound for the bond percolation threshold of the cubic lattice by a growth process approach, Continuity of the phase transition for planar random-cluster and Potts models with \({1 \leq q \leq 4}\), Universality for the random-cluster model on isoradial graphs, Self-avoiding walk on \(\mathbb{Z}^2\) with Yang-Baxter weights: universality of critical fugacity and 2-point function, Yang-Baxter random fields and stochastic vertex models, Harry Kesten's work in probability theory, Percolation and the pandemic, YANG–BAXTER FIELD FOR SPIN HALL–LITTLEWOOD SYMMETRIC FUNCTIONS, Unnamed Item, Critical correlation functions for the 4-dimensional weakly self-avoiding walk and \(n\)-component \(|\varphi|^4\) model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inhomogeneous bond percolation on square, triangular and hexagonal lattices
• Universality for bond percolation in two dimensions
• Three theorems in discrete random geometry
• Universality in the 2D Ising model and conformal invariance of fermionic observables
• Conformal invariance in random cluster models. I: Holomorphic fermions in the Ising model
• Discrete complex analysis on isoradial graphs
• On monochromatic arm exponents for 2D critical percolation
• Two-dimensional critical percolation: the full scaling limit
• Near-critical percolation in two dimensions
• The incipient infinite cluster in two-dimensional percolation
• The critical probability of bond percolation on the square lattice equals 1/2
• Critical exponents for two-dimensional percolation
• Scaling relations for 2D-percolation
• \(Q\)-dependent susceptibilities in ferromagnetic quasiperiodic \(Z\)-invariant Ising models
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Statistical Mechanics on Isoradial Graphs
• Advanced Statistical Mechanics
• Probability on Graphs
• Bond percolation on honeycomb and triangular lattices
• A note on percolation
• Percolation Probabilities on the Square Lattice
• Percolation on Penrose Tilings
• Percolation
• Rhombic embeddings of planar quad-graphs
• The Random-Cluster Model
• Potential theory on a rhombic lattice
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Discrete Riemann surfaces and the Ising model.