Vortex Dynamics and Entropic Coulomb Forces in Ising and Potts Antiferromagnets and Ice Models

Abstract

We study the dynamics of topological defects in the triangular Ising antiferromagnet, a related model on the square lattice equivalent to the six-vertex ice model, and the three-state antiferromagnetic Potts model on the square lattice. Since each of these models has a height representation in which defects are screw dislocations, we expect them to be attracted or repelled with an entropy-driven Coulomb force. In each case we show explicitly how this force is felt through local fields. We measure the force numerically, both by quenching the system to zero temperature and by measuring the motion of vortex pairs. For the three-state Potts model, we calculate both the force and the defect mobility, and find reasonable agreement with theory.