2021/04/30 by Bergfinnur Durhuus, Xavier Poncini, Jørgen Rasmussen +2
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Combinatorics #Computer science #Function (biology) #Geometry #Loop (graph theory) #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Physics #Planar #Spanning tree #Theoretical and Computational Physics #Topological and Geometric Data Analysis #Triangulation #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/ac2dfa
30 pages, v2: minor changes
openalex publication_date 2021/11/01 · arxiv created 2021/11/15 · arxiv updated 2021/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We introduce a dense and a dilute loop model on causal dynamical triangulations. Both models are characterised by a geometric coupling constant g and a loop parameter α in such a way that the purely geometric causal triangulation model is recovered for α = 1. We show that the dense loop model can be mapped to a solvable planar tree model, whose partition function we compute explicitly and use to determine the critical behaviour of the loop model. The dilute loop model can likewise be mapped to a planar tree model; however, a closed-form expression for the corresponding partition function is not obtainable using the standard methods employed in the dense case. Instead, we derive bounds on the critical coupling g c and apply transfer matrix techniques to examine the critical behaviour for α small.