Nonlinear response of relaxor ferroelectrics

The third order nonlinear response chi(3) of relaxor ferroelectrics has bee n calculated within the framework of a recently proposed spherical random b ond-random field model. It is assumed that the order parameter field can be associated with the polarization of nanosized polar clusters and is thus a continuous vector of variable length subject to a global spherical constra int. It is shown that for weak random fields the scaled third order nonline ar dielectric susceptiblity a(3) = chi(3)/chi(1)(4), where chi(1) is the li near susceptibility, has a narrow peak in the spherical glass phase without long range order, but there is no sharp freezing transition. In case of we ak random bonds the system behaves as a random field frustrated ferroelectr ic, with a(3) making a jump at the critical temperature.