Classifying magnetic and superfluid equilibrium states in magnets with the spin $s=1$

Based on the method of quasiaverages, we classify magnetic and superfluid equilibrium states in magnets with the spin $s=1$. Under certain simplifications, assumptions about the residual symmetry of degenerate states and the transformation properties of order parameter operators under transformations generated by additive integrals of motions lead to linear algebraic equations for a classification of the equilibrium means of the order parameters. We consider different cases of the magnetic $SO(3)$ or $SU(3)$ symmetry breaking and obtain solutions for the vector and tensor order parameters for particular forms of the parameters of the residual symmetry generators. We study the equilibriums of magnets with simultaneously broken phase and magnetic symmetries. We find solutions of the classification equations for superfluid equilibrium states and establish relations between the parameters of the residual symmetry generator that allow the thermodynamic coexistence of nonzero equilibrium means of the order parameters.