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Dominos and the Gaussian free field. (English) Zbl 1034.82021
Summary: We define a scaling limit of the height function on the domino tiling model (dimer model) on simply connected regions in \(\mathbb{Z}^2\) and show that it is the “massless free field”, a Gaussian process with independent coefficients when expanded in the eigenbasis of the Laplacian.

MSC:
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
60G60 Random fields
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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