  We consider a class of one-dimensional compass models with staggered
Dzyaloshinskii-Moriya exchange interactions in an external transverse magnetic
field. Based on the exact solution derived from Jordan-Wigner approach, we
study the excitation gap, energy spectra, spin correlations and critical
properties at phase transitions. We explore mutual effects of the staggered
Dzyaloshinskii-Moriya interaction and the magnetic field on the energy spectra
and the ground-state phase diagram. Thermodynamic quantities including the
entropy and the specific heat are discussed, and their universal scalings at
low temperature are demonstrated.
