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

Abstract

The three-dimensional abelian Higgs model has been argued to be dual to a scalar field theory with a global U(1) symmetry. We show that this duality, together with the scaling and universality hypotheses, implies a scaling law for the magnetic permeablity chi_m near the line of second order phase transition: chi_m ~ t^nu, where t is the deviation from the critical line and nu ~ 0.67 is a critical exponent of the O(2) universality class. We also show that exactly on the critical lines, the dependence of magnetic induction on external magnetic field is quadratic, with a proportionality coefficient depending only on the gauge coupling. These predictions provide a way for testing the duality conjecture on the lattice in the Coulomb phase and at the phase transion.

11 pages; updated references and small changes, published version

References in corpus (3)

• Pion Propagation near the QCD Chiral Phase Transition
• The order of the metal to superconductor transition
• Critical behaviour of the Ginzburg-Landau model in the type II region

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