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Critical dynamics of gauge systems: Spontaneous vortex formation in 2D superconductors

We examine the formation of vortices during the nonequilibrium relaxation of a high-temperature initial state of an Abelian-Higgs system. We equilibrate the scalar and gauge fields using gauge-invariant Langevin equations and relax the system by instantaneously removing thermal fluctuations. For couplings near critical we observe the formation of large clusters of like-sign magnetic vortices. Their appearance has implications for the dynamics of the phase transition, for the observed distribution of topological defects and for late-time phase ordering kinetics. We offer explanations for both the observed vortex densities and vortex configurations.