Critical behaviour of loop models on causal triangulations

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

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

Harvard

Durhuus, B, Poncini, X, Rasmussen, JØ & Ünel, M 2021, 'Critical behaviour of loop models on causal triangulations', Journal of Statistical Mechanics: Theory and Experiment, vol. 2021, no. 11, 113102. https://doi.org/10.1088/1742-5468/ac2dfa

APA

Durhuus, B., Poncini, X., Rasmussen, JØ., & Ünel, M. (2021). Critical behaviour of loop models on causal triangulations. Journal of Statistical Mechanics: Theory and Experiment, 2021(11), [113102]. https://doi.org/10.1088/1742-5468/ac2dfa

Vancouver

Durhuus B, Poncini X, Rasmussen JØ, Ünel M. Critical behaviour of loop models on causal triangulations. Journal of Statistical Mechanics: Theory and Experiment. 2021;2021(11). 113102. https://doi.org/10.1088/1742-5468/ac2dfa

Author

Durhuus, Bergfinnur ; Poncini, Xavier ; Rasmussen, JØrgen ; Ünel, Meltem. / Critical behaviour of loop models on causal triangulations. In: Journal of Statistical Mechanics: Theory and Experiment. 2021 ; Vol. 2021, No. 11.

Bibtex

@article{9e9ba8ce49f94a3d96085e5a9d2b9be3,

title = "Critical behaviour of loop models on causal triangulations",

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 gc and apply transfer matrix techniques to examine the critical behaviour for α small. ",

keywords = "Loop models and polymers, Random geometry, Solvable lattice models",

author = "Bergfinnur Durhuus and Xavier Poncini and J{\O}rgen Rasmussen and Meltem {\"U}nel",

note = "Publisher Copyright: {\textcopyright} 2021 IOP Publishing Ltd and SISSA Medialab srl.",

year = "2021",

doi = "10.1088/1742-5468/ac2dfa",

language = "English",

volume = "2021",

journal = "Journal of Statistical Mechanics: Theory and Experiment",

issn = "1742-5468",

publisher = "Institute of Physics Publishing Ltd",

number = "11",

}

RIS

TY - JOUR

T1 - Critical behaviour of loop models on causal triangulations

AU - Durhuus, Bergfinnur

AU - Poncini, Xavier

AU - Rasmussen, JØrgen

AU - Ünel, Meltem

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