### Abstract

The dynamically triangulated random surface (DTRS) approach to Euclidean quantum gravity in two dimensions is considered for the case of the elemental building blocks being quadrangles instead of the usually used triangles. The well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation are adapted to the problem of these dynamical quadrangulations. The thus defined ensemble of 4-valent graphs is appropriate for coupling to it the 6- and 8-vertex models of statistical mechanics. Using a series of extensive Monte Carlo simulations and accompanying finite-size scaling analyses, we investigate the critical behaviour of the 6-vertex F model coupled to the ensemble of dynamical quadrangulations and determine the matter related as well as the graph related critical exponents of the model.

Original language | English |
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Pages (from-to) | 312–346 |

Journal | Nuclear Physics B |

Volume | 719 |

Issue number | 3 |

DOIs | |

Publication status | Published - 25 Jul 2005 |

### Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Nuclear Physics B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nuclear Physics B, [719, 3, 2005] DOI: 10.1016/j.nuclphysb.2005.04.041 .© 2005, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

### Keywords

- Quantum gravity
- Ice-type vertex models
- Monte Carlo simulations
- Annealed disorder

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## Cite this

Weigel, M., & Janke, W. (2005). The F model on dynamical quadrangulations.

*Nuclear Physics B*,*719*(3), 312–346. https://doi.org/10.1016/j.nuclphysb.2005.04.041