Quantum compass model on the square and simple-cubic lattices

We use high-temperature series expansions to obtain thermodynamic properties of the quantum compass model, and to investigate the phase transition on the square and simple cubic lattices. On the square lattice we obtain evidence for a phase transition, consistent with recent Monte Carlo results. On the simple cubic lattice the same procedure provides no sign of a transition, and we conjecture that there is no finite temperature transition in this case.