  The effect of disorder on the quantum phase transitions induced by a
transverse field, anisotropy, and dimerization in XY spin chains is
investigated. The low-energy behavior near the critical point is described by a
Dirac-type equation with a random mass for which an exact analytic treatment is
possible. Results obtained for the dynamical critical exponent, the specific
heat, and transverse susceptibility agree with results recently obtained using
a real space renormalization group decimation technique, supporting Fisher's
claim that it is exact. A non-zero transverse field changes the universality
class of the anisotropy transition.

Condensed Matter