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Decimation on the Two Dimensionnal Ising Model : Non Gibbsianness at Low Temperature. Almost Gibbsianness or Weak Gibbsianness ?

Arnaud Le Ny (1998)

Publications mathématiques et informatique de Rennes

Determinant formulae for some tiling problems and application to fully packed loops

Philippe Di Francesco, Paul Zinn-Justin, Jean-Bernard Zuber (2005)

Annales de l’institut Fourier

We present a number of determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.

Die Polynome von Yang-Lee und ihre Nullstellen.

H. Carnal, I. Hueter (1990)

Elemente der Mathematik

Dimers and cluster integrable systems

Alexander B. Goncharov, Richard Kenyon (2013)

Annales scientifiques de l'École Normale Supérieure

We show that the dimer model on a bipartite graph $Γ$ on a torus gives rise to a quantum integrable system of special type, which we call acluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli space $Ł_{Γ}$ of line bundles with connections on the graph $Γ$ . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs $Γ_{1}$ and $Γ_{2}$ areequivalentif the Newton polygons of the corresponding partition functions...

Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices

David Cimasoni (2012)

Journal of the European Mathematical Society

Let $\sum$ be a flat surface of genus $g$ with cone type singularities. Given a bipartite graph $Γ$ isoradially embedded in $\sum$ , we define discrete analogs of the $2^{2 g}$ Dirac operators on $\sum$ . These discrete objects are then shown to converge to the continuous ones, in some appropriate sense. Finally, we obtain necessary and sufficient conditions on the pair $Γ \subset \sum$ for these discrete Dirac operators to be Kasteleyn matrices of the graph $Γ$ . As a consequence, if these conditions are met, the partition function of the dimer...

Dynamical critical exponent for two-species totally asymmetric diffusion on a ring.

Wehefritz-Kaufmann, Birgit (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Dynamics and Lieb-Robinson estimates for lattices of interacting anharmonic oscillators

L. Amour, P. Lévy-Bruhl, J. Nourrigat (2010)

Colloquium Mathematicae

For a class of infinite lattices of interacting anharmonic oscillators, we study the existence of the dynamics, together with Lieb-Robinson bounds, in a suitable algebra of observables.