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arXiv · 1204.3798

Coupling of hard dimers to dynamical lattices via random tensors

Valentin Bonzom·Harold Erbin
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Abstract

We study hard dimers on dynamical lattices in arbitrary dimensions using a random tensor model. The set of lattices corresponds to triangulations of the d-sphere and is selected by the large N limit. For small enough dimer activities, the critical behavior of the continuum limit is the one of pure random lattices. We find a negative critical activity where the universality class is changed as dimers become critical, in a very similar way hard dimers exhibit a Yang-Lee singularity on planar dynamical graphs. Critical exponents are calculated exactly. An alternative description as a system of `color-sensitive hard-core dimers' on random branched polymers is provided.

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Valentin Bonzom, Harold Erbin. 2012-04-17. Coupling of hard dimers to dynamical lattices via random tensors. https://doi.org/10.1088/1742-5468%2F2012%2F09%2Fp09009

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