Monte Carlo simulations show the superconductor-to-normal transition in U(1)^N lattice London models is discontinuous for N up to 7, with discontinuity strength non-monotonic in N, and the neutral superfluid transition is also first-order for N=3 and N=4.
Kleinert ,\ 10.1007/BF02754760 journal journal Lettere al Nuovo Cimento (1971-1985) \ volume 35 ,\ pages 405 ( year 1982 ) NoStop
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Phase transitions and composite order in $\mathrm{U}(1)^N$ lattice London models
Monte Carlo simulations show the superconductor-to-normal transition in U(1)^N lattice London models is discontinuous for N up to 7, with discontinuity strength non-monotonic in N, and the neutral superfluid transition is also first-order for N=3 and N=4.