20 citations · 53 across the 7 of their papers we have counts for
7 papers
Fock's dimer model on the Aztec diamond
Cédric Boutillier, Béatrice de Tilière
We consider the dimer model on the Aztec diamond with Fock's weights, which is gauge equivalent to the model with any choice of positive weight function. We prove an explicit, comp…
The Schwarzian octahedron recurrence (dSKP equation) II: geometric systems
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We consider nine geometric systems: Miquel dynamics, P-nets, integrable cross-ratio maps, discrete holomorphic functions, orthogonal circle patterns, polygon recutting, circle inte…
The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions
Niklas Christoph Affolter, Béatrice de Tilière, Paul Melotti
We prove an explicit expression for the solutions of the discrete Schwarzian octahedron recurrence, also known as the discrete Schwarzian KP equation (dSKP), as the ratio of two pa…
Minimal bipartite dimers and higher genus Harnack curves
Cédric Boutillier, David Cimasoni, Béatrice de Tilière
This paper completes the comprehensive study of the dimer model on infinite minimal graphs with Fock's weights [arXiv:1503.00289] initiated in [arXiv:2007.14699]: the latter articl…
The -invariant Ising model via dimers
Cédric Boutillier, Béatrice de Tilière, Kilian Raschel
The -invariant Ising model (Baxter in Philos Trans R Soc Lond A Math Phys Eng Sci 289(1359):315--346, 1978) is defined on an isoradial graph and has coupling constants depending…
The -invariant massive Laplacian on isoradial graphs
Cédric Boutillier, Béatrice de Tilière, Kilian Raschel
We introduce a one-parameter family of massive Laplacian operators defined on isoradial graphs, involving elliptic functions. We prove an explicit formula…
From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction
Béatrice de Tilière
Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph and the dimer model defined on a decorated version $\GD$ of this graph \c…