The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations

TL;DR

This paper provides an exact solution for the hard dimer model on 2D Causal Dynamical Triangulations, revealing multiple phases and their properties through amplitude calculations and scaling analysis.

Contribution

It introduces an exact solution for the hard dimer model on 2D CDT, identifying multiple phases and analyzing their properties and scaling limits.

Findings

Identification of gravity, tri-critical, and dense dimer phases.

Exact computation of cylinder and disk amplitudes.

Analysis of phase properties and scaling limits.

Abstract

We consider the model of hard dimers coupled to two-dimensional Causal Dynamical Triangulations (CDT) with all dimer types present and solve it exactly subject to a single restriction. Depending on the dimer weights there are, in addition to the usual gravity phase of CDT, two tri-critical and two dense dimer phases. We establish the properties of these phases, computing their cylinder and disk amplitudes, and their scaling limits.