The melting transition of a vortex lattice in the uniformly frustrated XY model with quasi-one-dimensional and quasi-two-dimensional coupling anisotropy

The uniformly frustrated XY model on the cubic lattice with an anisotropic coupling constant is studied numerically. Quasi-one-dimensional and quasi-two-dimensional systems are examined as models for a charge density wave in a ring crystal and a layer superconductor, respectively. The melting transition of a vortex lattice is investigated by means of non-equilibrium relaxation analysis. We find scaling behaviour of the relaxation with a power law, which indicates that the phase transition is of second order, in contrast to the first-order transition in the isotropic case. The critical exponents are estimated as β = 0.28 and zν = 2.3 for the quasi-one-dimensional system and β = 0.40 and zν = 2.9 for the quasi-two-dimensional system, and α≈0 for both cases. This implies that the universality classes of the two are different.