Universal Aspects of Deconfinement: Interfaces, Flux Tubes and Self-Duality in 2+1 Dimensions

We study center vortex free energies and 't Hooft's electric fluxes on the lattice in 2+1 dimensions, where SU(2) for example, is in the universality class of the 2d Ising model. This places a wealth of exact results at our fingertips. In particular, spacelike center vortices in SU(2) near criticality correspond to spin interfaces in the 2d Ising model, whose universal scaling functions are known exactly. We exploit this to locate the deconfinement transition with unprecedented precision and subsequently for a finite size scaling analysis, where the self-duality of the $2d$ spin model is reflected in a duality between the spacelike vortices and confining electric fluxes. The corresponding relation between the string tension and its dual in the high temperature phase is arguably the simplest example of a universal amplitude ratio. Around the transition, both can be efficiently extracted from the exact results with a global one-parameter fit which allows straightforward continuum extrapolation.