Exact solution of a lattice model of flux lines in superconductors

We consider a statistical mechanical model describing flux lines in type II superconductors by embedding the flux lines on a lattice wound on torus. The lines are nonintersecting and each loop of lines is associated with a fugacity z = −1. It is shown that the exact solution of this model leads to a second-order transition between the Meissner and the superconducting states as well as a first-order transition between the superconducting and the normal states.