Magnetic permeability of near-critical 3d abelian Higgs model and duality

The three-dimensional abelian Higgs model has been argued to be dual to ascalar field theory with a global U(1) symmetry. We show that this duality,together with the scaling and universality hypotheses, implies a scaling lawfor the magnetic permeablity chi_m near the line of second order phasetransition: chi_m ~ t^nu, where t is the deviation from the critical line andnu ~ 0.67 is a critical exponent of the O(2) universality class. We also showthat exactly on the critical lines, the dependence of magnetic induction onexternal magnetic field is quadratic, with a proportionality coefficientdepending only on the gauge coupling. These predictions provide a way fortesting the duality conjecture on the lattice in the Coulomb phase and at thephase transion.Comment: 11 pages; updated references and small changes, published versio