Simulations of the F model on planar φ 4 Feynman diagrams

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.