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.
|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||XXXLII International Symposium on Lattice Field Theory and Statistical Physics|
|Period||25/07/05 → 30/07/05|
Bibliographical noteThe full text is available from: http://pos.sissa.it/archive/conferences/020/251/LAT2005_251.pdf
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.