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Fock's dimer model on the Aztec diamond

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arxiv 2405.20284 v1 pith:OXIEFUJS submitted 2024-05-30 math.PR math.CO

Cédric Boutillier , Béatrice de Tilière This is my paper · ORCID
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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, compact formula for the inverse Kasteleyn matrix, thus extending numerous results in the case of periodic graphs. We also show an explicit product formula for the partition function; as a specific instance of the genus 0 case, we recover Stanley's formula. We then use our explicit formula for the inverse Kasteleyn matrix to recover, in a simple way, limit shape results; we also obtain new ones. In doing so, we extend the correspondence between the limit shape and the amoeba of the corresponding spectral curve of arXiv:2306.07482 to the case of non-generic weights.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quenched and Annealed CLTs for the one-periodic Aztec diamond in random environment

    math.PR 2025-10 conditional novelty 7.0 of 10

    Quenched height fluctuations in random-environment one-periodic Aztec diamonds converge almost surely to the Gaussian Free Field; annealed fluctuations are Gaussian with environment-dependent covariances.

  2. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

  3. Gaussian Free Field and Discrete Gaussians in Periodic Dimer Models

    math.PR 2025-02 conditional novelty 7.0 of 10

    Periodic Aztec diamond height fluctuations are shown to decompose into a Gaussian free field plus a discrete-Gaussian random harmonic component.

  4. Exactly Solvable Topological Phase Transition in a Quantum Dimer Model

    cond-mat.str-el 2026-01 conditional novelty 6.0 of 10

    A tunable triangular-lattice quantum dimer model is shown to undergo an exactly solvable continuous topological phase transition at edge weight α = 3, from a Z2 quantum spin liquid to a columnar ordered state.

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