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Correlation inequalities of GKS type for the Potts model
Correlation inequalities are presented for ferromagnetic Potts models with external field, using the random cluster representation of Fortuin and Kasteleyn, together with the FKG inequality. These results extend and simplify ...
The work of Lucio Russo on percolation
The contributions of Lucio Russo to the mathematics of percolation and disordered systems are outlined. The context of his work is explained, and its ongoing impact on current work is described and amplified.
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 ...