Two-Dimensional Vortex Lattice Melting

We report on a Monte-Carlo study of two-dimensional Ginzburg-Landau superconductors in a magnetic field which finds clear evidence for a first-order phase transition characterized by broken translational symmetry of the superfluid density. A key aspect of our study is the introduction of a quantity proportional to the Fourier transform of the superfluid density which can be sampled efficiently in Landau gauge Monte-Carlo simulations and which satisfies a useful sum rule. We estimate the latent heat per vortex of the melting transition to be $\sim 0.38 k_B T_M$ where $T_M$ is the melting temperature.Comment: 10 pages (4 figures available on request), RevTex 3.0, IUCM93-00

Grand-Canonical Ensemble of Random Surfaces with Four Species of Ising Spins

The grand-canonical ensemble of dynamically triangulated surfaces coupled to four species of Ising spins (c=2) is simulated on a computer. The effective string susceptibility exponent for lattices with up to 1000 vertices is found to be $\gamma = - 0.195(58)$. A specific scenario for $c > 1$ models is conjectured.Comment: LaTeX, 11 pages + 1 postscript figure appended, preprint LPTHE-Orsay 94/1