A rigorous bound on the critical exponent for the number of lattice trees, animals, and polygons.

DOI10.1007/BF02183684zbMath1080.82541MaRDI QIDQ1593196

Neal Madras

Publication date: 16 January 2001

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

critical exponentlattice treesubadditivitylattice animalself-avoiding polygon

Mathematics Subject Classification ID

Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

Related Items (18)

On the probability that self-avoiding walk ends at a given point ⋮ On the number of hexagonal polyominoes ⋮ Complex-time singularity and locality estimates for quantum lattice systems ⋮ Unnamed Item ⋮ On self-avoiding polygons and walks: the snake method via polygon joining ⋮ An upper bound on the number of self-avoiding polygons via joining ⋮ On the Asymptotic Enumeration of LEGO Structures ⋮ Rooted spiral trees on hyper-cubic lattices ⋮ On the number of entangled clusters ⋮ On the entropy of \(\mathsf{LEGO}^{\circledR}\) ⋮ Thoughts on lattice knot statistics ⋮ Lattice Polygons and Related Objects ⋮ Polygons and the Lace Expansion ⋮ Monte Carlo Methods for Lattice Polygons ⋮ Bounding the number of self-avoiding walks: Hammersley-Welsh with polygon insertion ⋮ Adsorption of lattice polymers with quenched topologies ⋮ A pattern theorem for lattice clusters ⋮ On the existence of critical exponents for self-avoiding walks

Cites Work

• Unnamed Item
• Unnamed Item
• Self-avoiding walk in five or more dimensions. I: The critical behaviour
• The number and size of branched polymers in high dimensions
• On the upper critical dimension of lattice trees and lattice animals
• Critical Behavior of Branched Polymers and the Lee-Yang Edge Singularity
• On the number of trees in Z^d
• Cell Growth Problems
• An inequality related to the isoperimetric inequality

This page was built for publication: A rigorous bound on the critical exponent for the number of lattice trees, animals, and polygons.