Renormalisation Group Theory of Branching Potts Interfaces

Abstract

We develop a field-theoretic representation for the configurations of an interface between two ordered phases of a q-state Potts model in two dimensions, in the solid-on-solid approximation. The model resembles the field theory of directed percolation and may be analysed using similar renormalisation group methods. In the one-loop approximation these reveal a simple mechanism for the emergence of a critical value q_c, such that for q<q_c the interface becomes a fractal with a vanishing interfacial tension at the critical point, while for q>q_c the interfacial width diverges at a finite value of the tension, indicating a first-order transition. The value of the Widom exponent for q<q_c within this approximation is in fair agreement with known exact values. Some comments are made on the case of quenched randomness. We also show that the q-> minus infinity limit of our model corresponds to directed percolation and that the values for the exponents in the one-loop approximation are in reasonable agreement with accepted values.