The F model on dynamical quadrangulations

Details The F model on dynamical quadrangulations The F model on dynamical quadrangulations

2004-09-08

arxiv.org/abs/hep-lat/0409028v2

Nucl.Phys. B719 (2005) 312-346

Physics

High Energy Physics

High Energy Physics - Lattice

LaTeX, 43 pages, 10 figures, 7 tables; substantially shortened and revised version as published, for more details refer to V1,

Scientific paper

10.1016/j.nuclphysb.2005.04.041

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.

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