 Solution

The shifted molecular field is the gradient ofThus $A=\mathrm{diag}(a+\alpha ,a-\alpha /2,a-\alpha /2)$.

If $\alpha <0$, the $x$ mode softens first atThe extensional flow already selects the $x$ axis, and ordering chooses one of its two polar directions. The transition is continuous and spontaneously breaks the remaining inversion symmetry $p_x\mapsto -p_x$.

If $\alpha >0$, the degenerate transverse modes soften first atThis transition is also continuous. The flow preserves rotations about the $x$ axis, while the ordered vector chooses an azimuthal direction in the $yz$ plane and spontaneously breaks that $SO(2)$ symmetry.