Using a frustrated $\mathrm{XY}$ model on a lattice with open-boundary conditions, we numerically study the magnetization change near a flux lattice melting transition at low fields. In both two and three dimensions, we find that the melting transition is followed at a higher temperature by the onset of large dissipation associated with the zero-field $\mathrm{XY}$ transition. It is characterized by the proliferation of vortex-antivortex pairs (in 2D) or vortex loops (in 3D). At the upper transition, there is a sharp increase in magnetization, in qualitative agreement with recent local Hall probe experiments.

• Received 31 March 1997

DOI:https://doi.org/10.1103/PhysRevLett.78.4629