New Universality Class for Ferroelectrics

For isotropic, centrosymmetric, ferroelectric systems described by an $n>\mathrm{}1\mathrm{}$ order parameter $\overrightarrow{\mathrm{p}}$, a new term in the Hamiltonian density, $w[{\overrightarrow{\mathrm{p}}}^2\nabla ·\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{p}}·\nabla ({\overrightarrow{\mathrm{p}}}^2\left)\right]$, is allowed. It is relevant, in the renormalization-group sense, in $d=4-\epsilon$ dimensions, when $n<\mathrm{}{n}_0=4-\frac{11\epsilon }{4}+O\left({\epsilon }^2\right)$. For $n<\mathrm{}{n}_0$, no stable fixed points exist. It is concluded that simple ferroelectric and ferromagnetic systems are not in the same universality class and thus do not necessarily exhibit identical critical behavior.