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Abstract
These lectures describe the behaviour of
two-dimensional superfluids, which differ from three-dimensional systems
in having phase transitions driven by
{\em thermally excited} vortices. Firstly, I will discuss
the Kosterlitz-Thouless-Berezinskii
(KTB) theory of the superfluid transition in helium films, which is due
to unbinding of vortex-antivortex pairs.
Next, I will describe the modifications of this transition
due to screening effects
at the zero field transition in superconductors. The transition of a
clean superconducting film in a perpendicular
magnetic field, caused by melting of the flux
lattice, will be discussed next.
This may also be of the KTB type, involving unbinding of
dislocations (with a second transition due to disclination unbinding
first discussed by Halperin and Nelson) or may be first order.
Finally, the case of a
dirty two-dimensional superconductor in a field will be discussed. This
has a vortex glass transition (analogous to the spin glass transition in
magnetic systems) at zero temperature. Results of recent experiments and
simulations which provide evidence for vortex glass behavior
will be discussed.
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