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A layered system of charges with logarithmic interaction parallel to thelayers and random dipoles in each layer is studied via a variational method andan energy rationale. These methods reproduce the known phase diagram for asingle layer where charges unbind by increasing either temperature or disorder,as well as a freezing first order transition within the ordered phase.Increasing interlayer coupling leads to successive transitions in which chargerods correlated in N>1 neighboring layers are unbounded by weaker disorder.Increasing disorder leads to transitions between different N phases. The methodis applied to flux lattices in layered superconductors in the limit ofvanishing Josephson coupling. The unbinding charges are point defects in theflux lattice, i.e. vacancies or interstitials. We show that short rangedisorder generates random dipoles for these defects. We predict and accuratelylocate a disorder-induced defect-unbinding transition with loss ofsuperconducting order, upon increase of disorder. While N=1 charges dominatefor most system parameters, we propose that in multi-layer superconductorsdefect rods can be realized.Comment: 26 pages, 6 figure

Disorder-induced transitions in layered Coulomb gases and application to flux lattices in superconductors