  We study theoretically many-body equilibrium magnetic phases and
corresponding thermodynamic characteristics of ultracold three-component
fermionic mixtures in optical lattices described by the SU(3)-symmetric
single-band Hubbard model. Our analysis is based on the generalization of the
exact diagonalization solver for multicomponent mixtures that is used in the
framework of the dynamical mean-field theory. It allows us to obtain a
finite-temperature phase diagram with the corresponding transition lines to
magnetically ordered phases at filling one particle per site (1/3 band filling)
in simple cubic lattice geometry. Based on the developed theoretical approach,
we also attain the necessary accuracy to study the entropy dependence in the
vicinity of magnetically ordered phases that allows us to make important
predictions for ongoing and future experiments aiming to approach and study
long-range-order phases in ultracold atomic mixtures.
