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We study a thermal and a transverse magnetic field response of a vortex linearray confined to a plane with a single columnar pinning defect. By integratingout ``bulk'' degrees of freedom away from the columnar defect we reduce thistwo-dimensional problem to a one-dimensional one, localized on the defect andexhibiting a long-range elasticity along the defect. We show that as a functionof temperature, for a magnetic field aligned with the defect this systemexhibits a one-dimensional analog of a roughening transition, with alow-temperature ``smooth'' phase corresponding to a vortex array pinned by thedefect, and a high-temperature ``rough'' phase in which at long scales thermalfluctuations effectively average away the pinning by the defect. We also findthat in the low-temperature pinned phase, the vortex lattice tilt response to atransverse magnetic field proceeds via a soliton proliferation transition,governed by an integrable sine-Hilbert equation and analogous to the well-knowncommensurate-incommensurate transition in sine-Gordon systems. Thedistinguishing feature here is the long-range nature of the one-dimensionalelasticity, leading to a logarithmic soliton energy and interaction. We predictthe transverse-field -- temperature phase diagram and discuss extension of ourresults to a bulk vortex array in the presence of a distribution of columnardefects.Comment: 27 pages, 17 figures; corrected typos, added reference

Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect