Critical behavior of the order parameter at antiferrodistortive transitions with cubic fluctuations

The temperature dependence of the generalized order parameter, namely the rotation angle of the Nb${\mathrm{O}}_6$ octahedron, at the antiferrodistortive transition in the perovskite crystal NaNb${\mathrm{O}}_3$, is derived through the high-resolution analysis of the second-order quadrupole shift of ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ NMR spectra. The second-order character of the transition and the small value of the apparent critical exponent for the order parameter are critically discussed in the framework of a renormalization-group approach for a system with an effective Hamiltonian of cubic symmetry and an anisotropic dispersion in the static structure factor.