Coupling of hard dimers to dynamical lattices via random tensors

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.

12 pages

References in corpus (4)

• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The 1/N expansion of colored tensor models
• Phase Transition in Dually Weighted Colored Tensor Models
• The Ising Model on Random Lattices in Arbitrary Dimensions

Cited by in corpus (6)

• Melons are branched polymers
• Double Scaling in Tensor Models with a Quartic Interaction
• Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions
• New 1/N expansions in random tensor models
• Towards a double-scaling limit for tensor models: probing sub-dominant orders
• Holography for Tensor models