Quantum phase transitions and backbending in even-even $N\sim90$ nuclei

We extend the classical Landau theory for rotating nuclei and show that the backbending in $^{162}Yb$, that comes about as a result of the two-quasiparticle alignment, is identified with the second order phase transition. We found that the backbending in $\mathrm{^{156}Dy}$, caused by the instability of $\gamma$-vibrations in the rotating frame, corresponds to the first order phase transition. We suggest the empirical rule to determine the type of the phase transition in rotating nuclei undergoing a backbending.