statistical mechanics - Why can't the density difference between the liquid and solid be an appropriate order parameter for liquid-to-solid transition?

The order parameter $\mathcal{O}$ in the case of a liquid-gas transition is the density difference $\mathcal{O}=\rho_{liq}-\rho_{gas}$.

But in the case of a liquid-to-solid transition, the order parameter $\mathcal{O}$ is not taken as the density difference $\mathcal{O}=\rho_{sol}-\rho_{liq}$. What is the reason? Is it just because the density difference is too small to measure?

Answer

There is no unique definition of "the" order parameter. However, we would like to use an order parameter that exhibits the full symmetry breaking pattern of the transition. If the transition corresponds to some symmetry $G$ breaking to a smaller symmetry $H$ then we want the order parameter to transform non-trivially under $G$, and exhibit the residual symmetry $H$. In the liquid-gas transition there are no continuous symmetries, and using the density is fine. In liquid-solid we break translational symmetry to a crystallographic symmetry. This requires a more complicated order parameter, like the F-trafo of the density correlator.