  We study the free energy landscape of a minimal model for relaxor
ferroelectrics. Using a variational method which includes leading correlations
beyond the mean-field approximation as well as disorder averaging at the level
of a simple replica theory, we find metastable paraelectric states with a
stability region that extends to zero temperature. The free energy of such
states exhibits an essential singularity for weak compositional disorder
pointing to their necessary occurrence. Ferroelectric states appear as local
minima in the free energy at high temperatures and become stable below a
coexistence temperature $T_c$. We calculate the phase diagram in the electric
field-temperature plane and find a coexistence line of the polar and non-polar
phases which ends at a critical point. First-order phase transitions are
induced for fields sufficiently large to cross the region of stability of the
metastable paraelectric phase. These polar and non-polar states have distinct
structure factors from those of conventional ferroelectrics. We use this
theoretical framework to compare and to gain physical understanding of various
experimental results in typical relaxors.
