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We study the minimizer of the d-wave Ginzburg-Landau energy in a specific class of functions. We show that the minimizer having distinct degree-one vortices is Holder continuous. Away from vortex cores, the minimizer converges uniformly to a canonical harmonic map. For a single vortex in the vortex core, we obtain the C 1 2 -norm estimate of the fourfold symmetric vortex solution. Furthermore, we prove the convergence of the fourfold symmetric vortex solution under different scales of .

Regularity of the Minimizer for the <i>D</i>-Wave Ginzburg-Landau Energy