  We introduce a spin ladder with antiferromagnetic Ising ZZ interactions along
the legs, and interactions on the rungs which interpolate between the Ising
ladder and the quantum compass ladder. We show that the entire energy spectrum
of the ladder may be determined exactly for finite number of spins 2N by
mapping to the quantum Ising chain and using Jordan-Wigner transformation in
invariant subspaces. We also demonstrate that subspaces with spin defects lead
to excited states using finite size scaling, and the ground state corresponds
to the quantum Ising model without defects. At the quantum phase transition to
maximally frustrated interactions of the compass ladder, the ZZ spin
correlation function on the rungs collapses to zero and the ground state
degeneracy increases by 2. We formulate a systematic method to calculate the
partition function for a mesoscopic system, and employ it to demonstrate that
fragmentation of the compass ladder by kink defects increases with increasing
temperature. The obtained heat capacity of a large compass ladder consisting of
2N=104 spins reveals two relevant energy scales and has a broad maximum due to
dense energy spectrum. The present exact results elucidate the nature of the
quantum phase transition from ordered to disordered ground state found in the
compass model in two dimensions.
