Title: Breaking universality in dimer models
Dimer models (random lozenge or domino tilings) on large planar domains exhibit universality behavior: local convergence to translation-invariant Gibbs measures, global fluctuations described by the Gaussian Free Field (GFF), and Airy line ensemble at the edges. In this talk, I discuss two mechanisms that break this universality while preserving some exactly solvable structure. First, applying a strong double-well potential parallel to one of the triangular lattice directions induces a new "waterfall" phase in lozenge tilings, where the 2D Gibbs structure collapses into a new 1D process with an emergent period-two structure. The exact solvability is powered by the q-Racah orthogonal polynomials. Second, randomizing edge weights in Aztec domino tilings (in a diagonally layered manner) deforms limit shapes. Moreover, it leads to non-GFF Brownian motion-like fluctuations living on root-N scale or the same constant scale as the GFF, depending on the variance scaling in the random edge weights. The exact solvability here comes from explicit annealed Schur generating functions.
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