Absence of a finite-temperature melting transition in the classical two-dimensional one-component plasma

Vortices in thin-film superconductors are often modeled as a system of part icles interacting via a repulsive logarithmic potential. Arguments are pres ented to show that the hypothetical (Abrikosov) crystalline state for such particles is unstable at any finite temperature against proliferation of sc reened disclinations. The correlation length of crystalline order is predic ted to grow as root 1/T as the temperature T is reduced to zero, in excelle nt agreement with our simulations of this two-dimensional system.