4-COLORING MODEL ON THE SQUARE LATTICE - A CRITICAL GROUND-STATE

We study critical properties of the four-coloring model, which is give n by the equal-weighted ensemble of all possible edge colorings of the square lattice with four different colors. We map the four-coloring m odel onto an interface model for which we propose an effective Gaussia n held theory, which allows us to calculate correlation functions of o perators in the coloring model. The critical exponents are given by th e stiffness of the interface, which we calculate exactly using recent results on the statistical topography of rough interfaces. Our numeric al exponents, hom Monte Carlo simulations of the four-coloring model, are in excellent agreement with the analytical calculations. These res ults support the conjecture that the scaling limit of the four-colorin g model is given by the SU(4)(k=1) Wess-Zumino-Witten model. Moreover, we show that our effective field theory is the free-field representat ion of the SU(4)(k=1) Wess-Zumino-Witten model. Finally, we discuss co nnections to loop models, and some predictions of finite temperature p roperties of a particular Potts model for which the four-coloring mode l is the ground state.