  We propose a definition of vorticity at inverse temperature \beta for Gibbs
states in quantum XY spin systems on the lattice by testing \exp[-\beta H] on a
complete set of observables ("one-point functions"). We show in particular that
it is independent of the choice of a particular basis. Imposing a compression
of Pauli matrices at the boudary, which stands for the classical environment,
we make some numerical simulations on finite lattices, and exhibit usual vortex
patterns.
