19 citations · 98 across the 40 of their papers we have counts for
6 papers · 1 filter
Self-avoiding walks and amenability
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of an infinite transitive graph is the exponential growth rate of the number of self-avoiding walks from a given origin. The relationship between…
Constrained percolation in two dimensions
Alexander Holroyd, Zhongyang Li
We prove absence of infinite clusters and contours in a class of critical constrained percolation models on the square lattice. The percolation configuration is assumed to satisfy…
Critical surface of the hexagonal polygon model
Geoffrey R. Grimmett, Zhongyang Li
The hexagonal polygon model arises in a natural way via a transformation of the 1-2 model on the hexagonal lattice, and it is related to the high temperature expansion of the Ising…
The 1-2 model
Geoffrey R. Grimmett, Zhongyang Li
The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constr…
Critical surface of the 1-2 model
Geoffrey R. Grimmett, Zhongyang Li
The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either or . There are three types of edge, and…
Connective constants and height functions for Cayley graphs
Geoffrey R. Grimmett, Zhongyang Li
The connective constant of an infinite transitive graph is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimm…