  It has recently been shown that the dissipative Hofstadter model (dissipative
quantum mechanics of an electron subject to uniform magnetic field and periodic
potential in two dimensions) exhibits critical behavior on a network of lines
in the dissipation/magnetic field plane. Apart from their obvious condensed
matter interest, the corresponding critical theories represent non-trivial
solutions of open string field theory, and a detailed account of their
properties would be interesting from several points of view. A subject of
particular interest is the dependence of physical quantities on the magnetic
field since it, much like $\theta_{\rm QCD}$, serves only to give relative
phases to different sectors of the partition sum. In this paper we report the
results of an initial investigation of the free energy, $N$-point functions and
boundary state of this type of critical theory. Although our primary goal is
the study of the magnetic field dependence of these quantities, we will present
some new results which bear on the zero magnetic field case as well.
