  The relaxors Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PZN) and
Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$ (PMN) have very similar properties based on the
dielectric response around the critical temperature $T_{c}$ (defined by the
structural transition under the application of an electric field). It has been
widely believed that these materials are quite different below $T_{c}$ with the
unit cell of PMN remaining cubic while in PZN the low temperature unit cell is
rhombohedral in shape. However, this has been clarified by recent high-energy
x-ray studies which have shown that PZN is rhombohedral only in the skin while
the shape of the unit cell in the bulk is nearly cubic. In this study we have
performed both neutron elastic and inelastic scattering to show that the
temperature dependence of both the diffuse and phonon scattering in PZN and PMN
is very similar. Both compounds show a nearly identical recovery of the soft
optic mode and a broadening of the acoustic mode below $T_{c}$. The diffuse
scattering in PZN is suggestive of an onset at the high temperature Burns
temperature similar to that in PMN. In contrast to PMN, we observe a broadening
of the Bragg peaks in both the longitudinal and transverse directions below
$T_{c}$. We reconcile this additional broadening, not observed in PMN, in terms
of structural inhomogeneity in PZN. Based on the strong similarities between
PMN and PZN, we suggest that both materials belong to the same universality
class and discuss the relaxor transition in terms of the three-dimensional
Heisenberg model with cubic anisotropy in a random field.
