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The critical current and melting temperature of a vortex system are analyzed.Calculations are made for a two dimensional film at finite temperature with twokinds of periodic pinning: hexagonal and Kagom\'e. A transport current paralleland perpendicular to the main axis of the pinning arrays is applied andmolecular dynamics simulations are used to calculate the vortex velocities toobtain the critical currents. The structure factor and displacements ofvortices at zero transport current are used to obtain the melting temperaturefor both pinning arrays. The critical currents are higher for the hexagonalpinning lattice and anisotropic for both pinning arrays. This anisotropy isstronger with temperature for the hexagonal array. For the Kagom\'e pinninglattice, our analysis shows a multi stage phase melting; that is, as weincrease the temperature, each different dynamic phase melts before reachingthe melting temperature. Both the melting temperature and critical currents arelarger for the hexagonal lattice, indicating the role for the interstitialvortices in decreasing the pinning strength.

Critical Currents and Melting Temperature of a Two-dimensional Vortex Lattice with Periodic Pinning