MEISSNER PHASE FOR A MODEL OF ORIENTED FLUX LINES

We consider a model of oriented, non-intersecting flux lines on the la ttice Z(d), where each flux line is assigned a Boltzmann factor omega per unit length and a fugacity y. We prove the existence of free energ y, both for y > 0 and for y = -1, and show that it is independent of y for y > 0. Using upper and lower bounds in terms of exactly solvable models, we rigorously establish that, for all y > 0, the model has a p hase transition at omega = 1/d. For omega < 1/d, we prove that the fre e energy and all bulk correlation functions vanish, implying the exclu sion of flux lines from the bulk. In this regime, we also show that th e Bur line density decays at least exponentially with distance from th e boundary.