  We prove that the bulk magnetization is equal to the edge current in the
thermodynamic limit for a large class of models of lattice fermions with
finite-range interactions satisfying local indistinguishability of the Gibbs
state, a condition known to hold for sufficiently high temperatures. Our result
implies that edge currents in such systems are determined by bulk properties
and are therefore stable against large perturbations near the boundaries.
Moreover, the equality persists also after taking the derivative with respect
to the chemical potential. We show that this form of bulk-edge correspondence
is essentially a consequence of homogeneity in the bulk and locality of the
Gibbs state. An important intermediate result is a new version of Bloch's
theorem for two-dimensional systems, stating that persistent currents vanish in
the bulk.
