### Abstract

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 |

### Fingerprint

### Bibliographical note

The full text is available from: http://pos.sissa.it/archive/conferences/020/251/LAT2005_251.pdf### Cite this

*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.

**Simulations of the F model on planar φ 4 Feynman diagrams.** / Janke, Wolfhard; Weigel, Martin.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Simulations of the F model on planar φ 4 Feynman diagrams

AU - Janke, Wolfhard

AU - Weigel, Martin

N1 - The full text is available from: http://pos.sissa.it/archive/conferences/020/251/LAT2005_251.pdf

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

M3 - Paper

ER -