An introduction to the dimer model

Abstract

Lecture notes from a minicourse given at the ICTP in May 2002.

References in corpus (3)

• A variational principle for domino tilings
• Alternating sign matrices and domino tilings
• Local statistics of lattice dimers

Cited by in corpus (56)

• Dimer models and toric diagrams
• Coulomb and Liquid Dimer Models in Three Dimensions
• Dimer models and the special McKay correspondence
• Gauge Theories at Resolved and Deformed Singularities using Dimers
• Relating Field Theories via Stochastic Quantization
• Introduction to Cluster Algebras. Chapters 1-3
• Bond percolation on isoradial graphs: criticality and universality
• Inhomogeneous bond percolation on square, triangular and hexagonal lattices
• Conformal invariance of isoradial dimer models & the case of triangular quadri-tilings
• Universality for bond percolation in two dimensions
• Dimer Models from Mirror Symmetry and Quivering Amoebae
• Universality for the random-cluster model on isoradial graphs
• Crystal Melting and Black Holes
• A Dimer ABC
• Rhombic embeddings of planar graphs with faces of degree 4
• Amoebas and Instantons
• The $Z$-invariant Ising model via dimers
• The $Z$-invariant massive Laplacian on isoradial graphs
• Local Statistics of Realizable Vertex Models
• Invariants of Toric Seiberg Duality
• Pattern densities in fluid dimer models
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Dimer representations of the Temperley-Lieb algebra
• Planar dimers and Harnack curves
• Domino shuffling for the Del Pezzo 3 lattice
• Rotational invariance in critical planar lattice models
• On FPL configurations with four sets of nested arches
• Consistency and Derangements in Brane Tilings
• Complexity problems in enumerative combinatorics
• A Note on Dimer Models and D-brane Gauge Theories
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Monte Carlo study of the hull distribution for the q=1 Brauer model
• Beyond Aztec Castles: Toric Cascades in the $d{P}_3$ Quiver
• Double scaling limit of the prismatic tensor model
• Calabi Yau algebras and weighted quiver polyhedra
• On Dimer Models and Closed String Theories
• Dungeons and Dragons: Combinatorics for the $d{P}_3$ Quiver
• Spectral Curve of Periodic Fisher Graphs
• Mahler Measure for a Quiver Symphony
• Deformations of Dimer Models
• Mutations of splitting maximal modifying modules: The case of reflexive polygons
• Tiling simply connected regions with rectangles
• Dimer Models, Free Fermions and Super Quantum Mechanics
• Connection probabilities in the double-dimer model -- the case of two connectivity patterns
• Critical Temperature of Periodic Ising Models
• Noncommutative mirror symmetry for punctured surfaces
• Domino shuffling on Novak half-hexagons and Aztec half-diamonds
• The expectation value of the number of loops and the left-passage probability in the double-dimer model
• Consistently melting crystals
• Cube moves for $s$-embeddings and $\alpha$-realizations
• Hypergeometric Systems in two Variables, Quivers, Dimers and Dessins d'Enfants
• Errata and Addenda to Mathematical Constants
• Fast domino tileability
• Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models
• Three theorems in discrete random geometry