An Analytical Analysis of CDT Coupled to Dimer-like Matter

TL;DR

This paper presents an analytical study of a restricted dimer model coupled to two-dimensional causal dynamical triangulations, revealing a phase transition and changes in geometric critical exponents.

Contribution

It introduces the first analytical solution of a matter model with two-dimensional interactions coupled to CDT using bijections with decorated trees.

Findings

Model exhibits a phase transition at negative dimer fugacity.

Critical exponent of the geometry changes at the transition.

Analytical solution provides new insights into matter-CDT interactions.

Abstract

We consider a model of restricted dimers coupled to two-dimensional causal dynamical triangulations (CDT), where the dimer configurations are restricted in the sense that they do not include dimers in regions of high curvature. It is shown how the model can be solved analytically using bijections with decorated trees. At a negative critical value for the dimer fugacity the model undergoes a phase transition at which the critical exponent associated to the geometry changes. This represents the first account of an analytical study of a matter model with two-dimensional interactions coupled to CDT.