Exact results for quantum phase transitions in random XY spin chains

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 for which an exact analytic treatment is possible. Results obtained for the dynamical critical exponent, the specific heat, and the transverse susceptibility agree with results recently obtained using a real space renormalization group decimation technique. A nonzero transverse field changes the universality class of the anisotropy transition.