  We describe a new order parameter for the confinement-deconfinement
transition in lattice SU(2) Yang-Mills theory. It is expressed in terms of
magnetic monopole field correlators represented as sums over sheets of center
vortices. Our construction establishes a link between "abelian" and "center
dominance". It avoids an inconsistency in the treatment of small scales present
in earlier definitions of monopole fields by respecting Dirac's quantization
condition for magnetic fluxes.
