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Vortices in thin-film superconductors are often modelled as a system ofparticles interacting via a repulsive logarithmic potential. Arguments arepresented to show that the hypothetical (Abrikosov) crystalline state for suchparticles is unstable at any finite temperature against proliferation ofscreened disclinations. The correlation length of crystalline order ispredicted to grow as $\sqrt{1/T}$ as the temperature $T$ is reduced to zero, inexcellent agreement with our simulations of this two-dimensional system.Comment: 3 figure

Absence of a Finite-Temperature Melting Transition in the Classical Two-Dimensional One-Component Plasma