U on a bounded, simply connected, two dimensional domain where ε → 0 and µε → µ ∈ [0, +∞]. Under the critical scaling, Gcsh ≈ |log ε | 2, we establish the Gamma limit when µ ∈ (0, +∞], and as a consequence we are able to compute the first critical field H1 = H1(U, µ) for the nucleation of a vortex. Finally, we show failure of Gamma convergence when µε → 0 (this includes the self-dual case). The method entails estimating in certain weak topologies the Jacobian J(uε) = det(∇uε) in terms of the Chern-Simons-Higgs energy Ecsh. 1
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