Critical behaviour of loop models on causal triangulations
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Critical behaviour of loop models on causal triangulations. / Durhuus, Bergfinnur; Poncini, Xavier; Rasmussen, JØrgen; Ünel, Meltem.
In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2021, No. 11, 113102, 2021.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Critical behaviour of loop models on causal triangulations
AU - Durhuus, Bergfinnur
AU - Poncini, Xavier
AU - Rasmussen, JØrgen
AU - Ünel, Meltem
N1 - Publisher Copyright: © 2021 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2021
Y1 - 2021
N2 - 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 gc and apply transfer matrix techniques to examine the critical behaviour for α small.
AB - 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 gc and apply transfer matrix techniques to examine the critical behaviour for α small.
KW - Loop models and polymers
KW - Random geometry
KW - Solvable lattice models
U2 - 10.1088/1742-5468/ac2dfa
DO - 10.1088/1742-5468/ac2dfa
M3 - Journal article
AN - SCOPUS:85119654835
VL - 2021
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
SN - 1742-5468
IS - 11
M1 - 113102
ER -
ID: 291621364