  A family of $\mathbb Z_n$-symmetric non-Hermitian models of Baxter was shown
by Fendley to be exactly solvable via a parafermionic generalization of the
Clifford algebra. We study these models with spatially random couplings, and
obtain several exact results on thermodynamic singularities as the
distributions of couplings are varied. We find that these singularities,
independent of $n$, are identical to those in the random transverse-field Ising
chain; correspondingly the models host infinite-randomness critical points.
Similarities in structure to exact methods for random Ising models, a
strong-disorder renormalization group, and generalizations to other models with
free spectra, are discussed.
