  The statistical mechanics of the flux-line lattice in extreme type-II super-
conductors is studied within the framework of the uniformly frustrated
anisotropic 3D XY-model. A finite-field counterpart of an Onsager vortex-loop
transition in extreme type-II superconductors renders the vortex liquid phase-
incoherent when the Abrikosov vortex lattice undergoes a first order melting
transition. For the filling fractions considered in this paper $f$ given by
$1/f=12,14,16,20,25,32,48,64,72,84,96,112$, and 128, the vortex liquid phase is
not describable as a liquid of well-defined field induced vortex lines. This is
due to the proliferation of thermally induced closed vortex-loops with dia-
meters of order the magnetic length in the problem, resulting in a "percolation
transition" driven by non-field induced vortices also transverse to the direc-
tion of the applied magnetic field. This immediately triggers flux-line lattice
melting and loss of phase-coherence in all direction. In a non-relativistic 2D
boson-analogy picture, this latter feature would correspond to a vanishing mass
of the bosons. Scaling functions for the specific heat are calculated in zero
and finite magnetic field. From this we conclude that the critical region is of
order 10% of $T_c$ for a mass anisotropy $\sqrt{M_z/M}=3$, and increases with
increasing mass anisotropy. The entropy jump at the melting transition is cal-
culated as a function of magnetic field for a mass-ansitropy slightly lower
than that in $YBCO$, and found to be $\Delta S=0.1k_B$ per vortex panncake,
independent of the magnetic field for the filling fractions considered here.
This is slightly lower than experimental values of $\Delta S \approx 0.4k_B$
found experimentally for $YBCO$. We attribute this to the slightly lower mass
anisotropy used in our simulations.
