  We introduce a new method, based on the recently developed random tensor
theory, to study the p-spin glass model with non-Gaussian, correlated disorder.
Using a suitable generalization of Gurau's theorem on the universality of the
large N limit of the p-unitary ensemble of random tensors, we exhibit an
infinite family of such non-Gaussian distributions which leads to same low
temperature phase as the Gaussian distribution. While this result is easy to
show (and well known) for uncorrelated disorder, its robustness with respect to
strong quenched correlations is surprising. We show in detail how the critical
temperature is renormalized by these correlations. We close with a speculation
on possible applications of random tensor theory to finite-range spin glass
models.
