  In a recent breakthrough [arXiv:2301.04112], Chatterjee proved site disorder
chaos in the Edwards-Anderson (EA) short-range spin glass model utilizing the
Hermite spectral method. In this paper, we demonstrate the further usefulness
of this Hermite spectral approach by extending the validity of site disorder
chaos in three related spin glass models.
  The first, called the mixed even $p$-spin short-range model, is a
generalization of the EA model where the underlying graph is a deterministic
bounded degree hypergraph consisting of hyperedges with even number of
vertices. The second model is the diluted mixed $p$-spin model, which is
allowed to have hyperedges with both odd and even number of vertices. For both
models, our results hold under general symmetric disorder distributions. The
main novelty of our argument is played by an elementary algebraic equation for
the Fourier-Hermite series coefficients for the two-spin correlation functions.
It allows us to deduce necessary geometric conditions to determine the
contributing coefficients in the overlap function, which in spirit is the same
as the crucial Lemma 1 in [arXiv:2301.04112]. Finally, we also establish
disorder chaos in the L\'evy model with stable index $\alpha \in (1, 2)$.
