We have numerically studied the statics and dynamics of a model
three-dimensional vortex lattice at low magnetic fields. For the statics we use
a frustrated 3D XY model on a stacked triangular lattice. We model the dynamics
as a coupled network of overdamped resistively-shunted Josephson junctions with
Langevin noise. At low fields, there is a weakly first-order phase transition,
at which the vortex lattice melts into a line liquid. Phase coherence parallel
to the field persists until a sharp crossover, conceivably a phase transition,
near Tℓ>Tm which develops at the same temperature as an infinite
vortex tangle. The calculated flux flow resistivity in various geometries near
T=Tℓ closely resembles experiment. The local density of field induced
vortices increases sharply near Tℓ, corresponding to the experimentally
observed magnetization jump. We discuss the nature of a possible transition or
crossover at Tℓ(B) which is distinct from flux lattice melting.Comment: Updated references. 46 pages including low quality 25 eps figures.
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http://www.physics.ohio-state.edu:80/~ryu/ for better figures and additional
movie files from simulations. To be published in Physical Review B1 01Jun9