A VORTEX MODEL WITH SUPERFLUID AND TURBULENT PERCOLATION

Simple lattice vortex models are presented that exhibit vortex percolation along lines in a temperature/chemical potential plane. Parts of these lines can be identified with the percolation threshold at the inertial range of turbulence, and other parts are analogous to the transition in a three-dimensional XY model that may model the lambda transition in superfluidity. Flory exponents at percolation are calculated; for nonnegative temperatures, their values approximate the standard Flory value, and are approximately constant along the transition lines, in agreement with recent conjectures. Conclusions regarding coherent structures in turbulence are also reached.