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The Planar Ising Model and Total Positivity
(SpringerJournal of Statistical Physics, 2017-01-01)
A matrix is called totally positive (resp. totally nonnegative) if all its minors are positive (resp. nonnegative). Consider the Ising model with free boundary conditions and no external field on a planar graph G. Let ...
The 1-2 model
(American Mathematical SocietyIn the Tradition of Ahlfors–Bers, VII, 2017)
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 constrained to have degree either 1 or 2. It was ...