Finite Temperature Phase Transitions in the SU$(N)$ Hubbard model

We investigate the SU($N$) Hubbard model for the multi-component fermionic optical lattice system, combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method. We obtain the finite temperature phase diagrams with $N\le 6$ and find that low temperature properties depends on the parity of the components. The magnetically ordered state competes with the correlated metallic state in the system with the even number of components $(N\ge 4)$, yielding the first-order phase transition. It is also clarified that, in the odd-component system, the ordered state is realized at relatively lower temperatures and the critical temperature is constant in the strong coupling limit.