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Monte-Carlo simulations in conjunction with finite-size scaling analysis areused to investigate the $(H,T)$-phase diagram in uniaxial anisotropic high-$T_c$ superconductors, both in zero magnetic field and in intermediate magneticfields for various mass-anisotropies. The model we consider is the uniformlyfrustrated anisotropic Villain Model. In zero magnetic field, and for allanisotropies considered, we find one single second order phase transition,mediated by an Onsager vortex-loop blowout. This is the superconductor-normalmetal transition.A comparison with numerical simulations and a critical scalinganalysis of the zero-field loop-transition yields the same exponent of the loopdistribution function at the critical point. In the intermediate magnetic fieldregime, we find two anomalies in the specific heat. The first anomaly at atemperature $T_m$ is associated with the melting transition of the flux-linelattice. The second anomaly at a temperature $T_z$ is one where phase coherencealong the field direction is destroyed. We argue that $T_m=T_z$ in thethermodynamic and continuum limit. Hence, there is no regime where the fluxline lattice melts into a disentangled flux-line liquid. The loss of phasecoherence parallel to the magnetic field in the sample is argued to be due tothe proliferation of closed non-field induced vortex loops on the scale of themagnetic length in the problem, resulting in flux-line cutting andrecombination. In the flux-line liquid phase, therefore, flux-lines appear nolonger to be well defined entities. A finite-size scaling analysis of the deltafunction peak specific heat anomaly at the melting transition is used toextract the discontinuity of the entropy at the melting transition.This entropydiscontinuity is found to increase rapidly with mass-anisotropy.Comment: 22 pages, 11 figures included, to be published in Phys. Rev. B, 57  xxx (1998

physical review. b, condensed matter

Onsager loop transition and first-order flux-line lattice melting in high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductors

Onsager loop transition and first-order flux-line lattice melting in high-Tcsuperconductors