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Possible phases and the B-T phase diagram of interlayer Josephson vorticesinduced by a magnetic field parallel to the superconducting layers areinvestigated by Monte Carlo simulations based on the anisotropic, frustrated XYmodel. While for low magnetic fields and small anisotropy parameters a singlefirst-order transition is observed similarly to the melting of Abrikosov (orpancake) vortex lattice, an intermediate phase, characterized by decoupled,two-dimensional (2D) quasi long-range crystalline order (QLRCO) andsuperconductivity, is found at high magnetic fields and large anisotropyparameters. Combining the simulation results with a symmetry argument, it isrevealed that this intermediate phase is of Kosterlitz-Thouless (KT) type, andthe melting of 2D quasi Josephson vortex lattices and suppression ofsuperconductivity is a KT transition. Evolution of the intermediate phase tothe low-temperature phase of 3D LRCO is second order and belongs to the 3D XYuniversality class. The three phase boundaries merge at a multicritical point.It is revealed that decoupling of the 3D Josephson vortex lattice into the 2Dphase is triggered by hops of Josephson flux lines across superconductinglayers activated by thermal fluctuations. The equilibrium phase diagram withthe KT phase at high magnetic fields and large anisotropy parameters isconsistent with the peculiar Lorentz-force-independent dissipation observed inhighly anisotropic high-Tc superconductor Bi2Sr2CaCu2O(8+y) by Iye et al.(Physica 159C, 433 (1989)).Comment: 13 pages, 14 figures. to appear in PR

Decoupled two-dimensional superconductivity and continuous melting transitions in layered superconductors immersed in a parallel magnetic field