An Analytical Analysis of CDT Coupled to Dimer-like Matter

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.

12 pages, many figures, shortened, as published

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Cited by in corpus (14)

• Trees and spatial topology change in CDT
• On the Quantum Geometry of Multi-critical CDT
• Quantum Flatness in Two-Dimensional CDT Quantum Gravity
• 2d CDT with gauge fields
• Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations
• A model for emergence of space and time
• A restricted dimer model on a 2-dimensional random causal triangulation
• Growth of uniform infinite causal triangulations
• Critical behaviour of loop models on causal triangulations
• Criticality at absolute zero from Ising model on two-dimensional dynamical triangulations
• The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
• Critical region for an Ising model coupled to causal dynamical triangulations
• Endeavours in Discrete Lorentzian Geometry; A thesis in five papers
• Analytical approaches to 2D CDT coupled to matter