Dimers with layered disorder

Quentin Moulard; Fabio Toninelli

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arXiv · 2507.11964

Dimers with layered disorder

Quentin Moulard·Fabio Toninelli

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Abstract

We study the dimer model on the square grid, with quenched random edge weights. Randomness is chosen to have a layered structure, similar to that of the celebrated McCoy-Wu disordered Ising model. Disorder has a highly non-trivial effect and it produces an essential singularity of the free energy, with $e^{-\sqrt{\rm distance}}$ decay of dimer-dimer correlations, at a point of the ``liquid'' (or ``massless'') phase where the homogeneous dimer model has instead a real analytic free energy and correlations decaying like $1/({\rm distance})^2$. Moreover, at a point where the homogeneous model has a transition between a massive (gaseous) and massless (liquid) phase, the critical exponent 3/2 (Pokrovsky-Talapov law), characteristic of the transition between the two regimes, is modified by disorder into an exponent that ranges continuously between 3/2 and infinity.

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Quentin Moulard, Fabio Toninelli. 2025-07-16. Dimers with layered disorder. https://arxiv.org/abs/2507.11964

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