Someone argues: "A magnet's order parameter changes sign under a reversal of the…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Order, broken symmetry and collective behaviour · Soft condensed matter

Soft Matter at the Thermal Scale, Ch Nematic order and the isotropic-nematic transition

Problem

Someone argues: "A magnet's order parameter mm changes sign under a reversal of the applied field or of the magnetisation itself; because m→−mm \to -m maps the disordered state onto an equally valid state, the Landau free energy of a magnet contains only even powers of mm, and this is what forces the ferromagnetic transition to be continuous. The nematic order parameter SnS_{\rm n} also flips sign when the molecules pack side-on to the director (Sn<0S_{\rm n} < 0) instead of end-on (Sn>0S_{\rm n} > 0), so by the same reasoning the nematic free energy should contain only even powers of SnS_{\rm n}, and the isotropic-nematic transition should also be continuous." Find the error in this argument, given that 5CB is measured to jump to Sn≈0.3S_{\rm n} \approx 0.3 exactly at TNIT_{\rm NI}.

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