Irrelevant variables, Landau expansions, and cubic anisotropy

A two-component spin system (${\phi }_1$,${\phi }_2$) with cubic anisotropy is studied using a Landau expansion truncated at order eight (${\phi }^8$ theory). The symmetry of the ordered phases is primarily fixed by the coefficient of ${\phi }_1^2$ ${\phi }_2^2$ in the expansion. While constant within a ${\phi }^4$ theory this coefficient becomes temperature dependent within a ${\phi }^8$ theory. A systematic investigation of the minima of the free energy is carried out as a function of the various Landau coefficients. Comparison of ${\phi }^4$ and ${\phi }^8$ theories shows that inclusion of sixth- and eighth-degree terms does not only generate a new symmetry breaking but changes the relative energy of the previous minima. Experimental data on the rare-earth molybdate ${\mathrm{Tb}}_2$(${\mathrm{MoO}}_4$ ${)}_3$ are shown to fit exactly a ${\phi }^8$ theory.