Lattice Coulomb gas representations of two-dimensional problems

Abstract

Many of the standard two-dimensional problems of statistical physics can be transformed into 'Coulomb gas' problems in which there are two kinds of 'charges' represented by integers n and m. Such a transformation works for the Ising model, the three- and four-state Potts models, the Ashkin-Teller model, any many others. In general the n-n and m-m interactions have the Coulomb character in which the interaction is, for large separations, proportional to the logarithm of the distance. On the other hand, the n(r)-m(R) interaction is for large distances proportional to i times the angle Phi (r-R) which measures the angular position of R relative to r. This latter interaction is akin to that between a magnetic monopole and an electric charge.