Finite-size effects of the helicity modulus in the two-dimensional classical XY model

Abstract

A systematic numerical study of the relevant finite-size effects of the helicity modulus for the two-dimensional classical XY model demonstrates the usefulness of this quantity as a means of obtaining information about Kosterlitz-Thouless type phase transitions. In this way, one does not have to compute correlation functions on finite lattices, and fit or compare the data thus obtained to theoretical scaling predictions, which only pertain to extremely large lattices. The approach may have many applications to systems of current interest that exhibit XY-like phase transitions.