We consider the quantum field theory of a single, immobile, spin S hole cou
pled to a two-dimensional antiferromagnet at a bulk quantum critical point
between phases with and without magnetic long-range order. We present an al
ternative derivation of its two-loop beta function, the results agree compl
etely with earlier work [Phys. Rev. B 61 (2000) 15152], and also determine
a new anomalous dimension of the hole creation operator. (C) 2001 Published
by Elsevier Science B.V.