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Vortex-lattice melting in two-dimensional superconductors in intermediate fields

To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the melting transition in higher fields is significantly weakened with decreasing the field. Nevertheless, a genuine crossover to the consecutive continuous melting picture intervened by a hexatic liquid is not found within the use of the GL model.