19 citations · 98 across the 40 of their papers we have counts for
4 papers · 1 filter
Positive speed self-avoiding walks on graphs with more than one end
Zhongyang Li
A self-avoiding walk (SAW) is a path on a graph that visits each vertex at most once. The mean square displacement of an -step SAW is the expected value of the square of the dis…
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…
Critical Temperature of Periodic Ising Models
Zhongyang Li
A periodic Ising model is one endowed with interactions that are invariant under translations of members of a full-rank sublattice of . We give an exac…
Local Statistics of Realizable Vertex Models
Zhongyang Li
We study planar "vertex" models, which are probability measures on edge subsets of a planar graph, satisfying certain constraints at each vertex, examples including dimer model, an…