Coupling of hard dimers to dynamical lattices via random tensors

TL;DR

This paper investigates how hard dimers interact with dynamical lattices across various dimensions using random tensor models, revealing critical behaviors and universality class changes at specific activities.

Contribution

It introduces a random tensor model approach to study hard dimers on dynamical lattices in arbitrary dimensions, identifying critical points and universality class transitions.

Findings

Critical behavior matches pure random lattices at low dimer activity.

A negative critical activity changes the universality class, similar to Yang-Lee singularity.

Critical exponents are calculated exactly.

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.