  The melting and magnetic disordering of the skyrmion lattice in the quantum
Hall system at filling factor $\nu\approx 1$ are studied. A
Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to
describe the coupled magnetic and translational degrees of freedom. The
non-trivial magnetic properties of the skyrmion system stem from the in-plane
components of the non-collinear magnetization in the vicinity of skyrmions,
which are described by an antiferromagnetic XY model. In a Coulomb gas
formulation the `particles' are the topological defects of the XY model
(vortices) and of the lattice (dislocations and disclinations). The latter
frustrate the antiferromagnetic order and acquire fractional vorticity in order
to minimize their energy. We find a number of melting/disordering scenarios for
various lattice types. While these results do not depend on a particular model,
we also consider a simple classical model for the skyrmion system. It results
in a rich T=0 phase diagram. We propose that the triangular and square skyrmion
lattices are generically separated by a centered rectangular phase in the
quantum Hall system.
