Emergence of U(1) symmetry in the 3D XY model with Zq anisotropy

Understand

We study the three-dimensional XY model with a Z_q anisotropic term.

• At temperatures T < Tc this dangerously irrelevant perturbation is relevant only above a length scale Lambda, which diverges as a power of the correlation length; Lambda ~ xi^a_q.
• Below Lambda the order parameter is U(1) symmetric.
• We derive the full scaling function controlling the emergence of U(1) symmetry and use Monte Carlo results to extract the exponent a_q for q=4,...,8.