Freezing effects in the two-dimensional one-component plasma and in thin-film type-II superconductors

We present results of Monte Carlo simulations of the two dimensional one-component plasma and of the Ginzberg-Landau model in the lowest Landau level approximation, with both charges and vortices respectively confined within a disc. In both models we see that as the temperature is reduced, oscillations in the radial density develop which spread into the bulk from the edge of the disc. The amplitude of these oscillations grows as the temperature is lowered and the length scale over which the oscillations occurs is the same as the correlation length for local crystalline order at that temperature. At temperatures similar to those where earlier studies have reported a first-order fluid-crystal phase transition, the correlation length is comparable to the linear dimensions of the samples studied, which suggests that finite size effects will be affecting the accuracy of their conclusions.