### Abstract

The 6-vertex F model on the square lattice exhibits a critical line with central chargeC = 1, terminating
in a critical point of the Kosterlitz-Thouless type. As such, its coupling to two-dimensional
quantum gravity by placing it onto the dynamically triangulated random surfaces (DTRS) of the
simplicial formulation yields an interesting realization of the limiting case C = 1 where the continuum
description of quantum gravity plus matter fields in two dimensions breaks down. Technically,
since the general 6- and 8-vertex models of statistical mechanics are defined with respect
to four-valent lattices, the model has to be coupled to dynamical quadrangulations. Generalizing
the well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation
to the case of these random lattices made of squares, we present extensive numerical results
for the critical-point properties of the coupled system, including the matter related as well as the
graph related critical exponents of the model.

Original language | English |
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Publication status | Published - 2005 |

Event | XXXLII International Symposium on Lattice Field Theory and Statistical Physics - Trinity College, Dublin, Ireland Duration: 25 Jul 2005 → 30 Jul 2005 |

### Conference

Conference | XXXLII International Symposium on Lattice Field Theory and Statistical Physics |
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Country | Ireland |

City | Dublin |

Period | 25/07/05 → 30/07/05 |

### Bibliographical note

The full text is available from: http://pos.sissa.it/archive/conferences/020/251/LAT2005_251.pdf## Fingerprint Dive into the research topics of 'Simulations of the F model on planar φ 4 Feynman diagrams'. Together they form a unique fingerprint.

## Cite this

Janke, W., & Weigel, M. (2005).

*Simulations of the F model on planar φ 4 Feynman diagrams*. Paper presented at XXXLII International Symposium on Lattice Field Theory and Statistical Physics, Dublin, Ireland.