Order in Quantum Compass and Orbital e_{g} Models

We investigate thermodynamic phase transitions in the compass model and in e_{g} orbital model on an infinite square lattice by variational tensor network renormalization (VTNR) in imaginary time. The onset of nematic order in the quantum compass model is estimated at _{c}/J=0.0606(4). For the e_{g} orbital model one finds: (i) a very accurate estimate of _{c}/J=0.3566± 0.0001 and (ii) the critical exponents in the Ising universality class. Remarkably large difference in frustration results in so distinct values of _{c}, while entanglement influences the quality of _{c} estimation.