Area-weighted moments of convex polygons on the square lattice

Abstract

When constructing series expansions for the zero-field partition function of the q-state Potts model on the square lattice using the finite-lattice method, the series can be extended by one term by adding a correction of (q-1) times the number of convex polygons of an appropriate order. By virtue of duality, such corrections apply for both high- and low-temperature series. For low-temperature series, corrections to the field-dependent partition function are of the same order in the temperature variable as the zero-field correction. The general corrections are given by area-weighted moments of the number of convex polygons. The authors obtain conjectured closed-form expressions for the two ge..