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Critical Surface of the Hexagonal Polygon Model
(SpringerJournal of Statistical Physics, 2016-05-01)
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 model. There are three types of edge, and ...
Connective constants and height functions for Cayley graphs
(American Mathematical SocietyTransactions of the American Mathematical Society, 2017-03-31)
The connective constant $μ$($G$) of an infinite transitive graph $G$ is the exponential growth rate of the number of self-avoiding walks from a given origin. In earlier work of Grimmett and Li, a locality theorem was proved ...
Critical surface of the 1-2 model
The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. There are three edge directions, and three corresponding parameters a, b, c. It ...