  We compute the critical exponents associated with a magnetic line defect in
the critical 3D Ising model. From the result, we deduce the anomalous dimension
of the fermion operator in the z = 1 scaling regime of a Fermi surface coupled
to a O(1) Wilson-Fisher fixed point. We introduce a generalization of the Wolff
cluster algorithm to O(N) spin systems with a background magnetic field.
