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We study the impact of the non-analytic reconstruction of vortex cores onstatic vortex structures in weakly coupled superfluids. We show that inrotating two-dimensional systems, the Abrikosov vortex lattice is unstable tovortex core deformation: Each zero of the wave function becomes a cut of finitelength. The directors characterizing the orientations of the cuts arethemselves ordered in superstructures due either to surface effects or tointeraction with shear deformations of the lattice (spiral structure). Similarinstability may be also observable in clean superconducting films.

Instability of Abrikosov lattice due to nonanalytic core reconstruction of vortices in Bosonic superfluids