Kosterlitz-Thouless phase and continuous melting transition in layered superconductors immersed in a parallel magnetic field

B-T phase diagram and phase transitions of interlayer Josephson vortices are investigated. For magnetic fields above a critical value, we find a Kosterlitz-Thouless (KT) type intermediate phase characterized by in-plane two-dimensional, quasi long-range orders (QLROs) of vortex alignment and superconductivity. The transformation to high-temperature normal phase is a KT transition. The evolution to low-temperature phase of three-dimensional (3D) LRO of vortex alignment is a second-order phase transition in the 3D XY universality class. For low magnetic fields, a single first-order melting transition of the Josephson vortex lattice is observed. The present study therefore indicates a multicritical point in the B-T phase diagram.