  We study conformal field theories describing two massless one-dimensional
fields interacting at a single spatial point. The interactions we include are
periodic functions of the bosonized fields separately plus a ``magnetic''
interaction that mixes the two fields. Such models arise in open string theory
and dissipative quantum mechanics and perhaps in edge state tunneling in the
fractional quantized Hall effect. The partition function for such theories is a
Coulomb gas with interchange phases arising from the magnetic field. These
``fractional statistics'' have a profound effect on the phase structure of the
Coulomb gas. In this paper we present new exact and approximate results for
this type of generalized Coulomb gas.
