Dimers with layered disorder
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916845561315328 |
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| author | Moulard, Quentin Toninelli, Fabio |
| author_facet | Moulard, Quentin Toninelli, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimers with layered disorder Moulard, Quentin Toninelli, Fabio Probability 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. |
| title | Dimers with layered disorder |
| topic | Probability |
| url | https://arxiv.org/abs/2507.11964 |