The emergence of the electrostatic field as a Feynman sum in random tilings with holes

DOI10.1090/S0002-9947-10-05087-7zbMath1198.82021arXiv0710.4490OpenAlexW2964329672MaRDI QIDQ4930026

Mihai Ciucu

Publication date: 27 September 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.4490

zbMATH Keywords

random lozenge tilingslattice triangles

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Asymptotic enumeration (05A16) Applications of statistical mechanics to specific types of physical systems (82D99) Limit theorems in probability theory (60F99)

Related Items (12)

Macroscopically separated gaps in dimer coverings of Aztec rectangles ⋮ Interactions between interleaving holes in a sea of unit rhombi ⋮ Lozenge tilings of hexagons with removed core and satellites ⋮ The interaction of a gap with a free boundary in a two dimensional dimer system ⋮ Exact solution of the 2d dimer model: corner free energy, correlation functions and combinatorics ⋮ Three interactions of holes in two dimensional dimer systems ⋮ Lozenge tilings with gaps in a \(90\degree\) wedge domain with mixed boundary conditions ⋮ The interaction of collinear gaps of arbitrary charge in a two dimensional dimer system ⋮ Correlation of a macroscopic dent in a wedge with mixed boundary conditions ⋮ The effect of microscopic gap displacement on the correlation of gaps in dimer systems ⋮ Dimers and families of Cauchy-Riemann operators I ⋮ A statistical model of current loops and magnetic monopoles

Cites Work

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• Rotational invariance of quadromer correlations on the hexagonal lattice
• The shape of a typical boxed plane partition
• Local statistics of lattice dimers
• Local statistics for random domino tilings of the Aztec diamond
• Dimers and amoebae
• A variational principle for domino tilings
• Dimer packings with gaps and electrostatics
• Conway's Tiling Groups
• The scaling limit of the correlation of holes on the triangular lattice with periodic boundary conditions
• Statistical Mechanics of Dimers on a Plane Lattice. II. Dimer Correlations and Monomers
• A random tiling model for two dimensional electrostatics

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