2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106944Systems of nearly parallel, slender vortex filaments in which angular momentum is conserved are an important simplification of the Navier-Stokes equations where turbulence can be studied in statistical equilibrium. We study the canonical Gibbs distribution based on the Klein-Majda-Damodaran (KMD) model and find a divergence in the mean square vortex position from that of the point vortex model of Onsager at high temperature. We subsequently develop a free energy equation based on the non-interacting case, with a spherical constraint, which we approximate using the method of Kac-Berlin, adding a mean field term for logarithmic interaction. This free energy equation, we use to predict the Monte Carlo results.13 pages, 5 figures; major revisions in theoretical section; slight change of numerical results from L=20 to L=100; typos corrected in free-energy sectionStatistical MechanicsSuperconductivitytext