  We present numerical studies of fermion and boson models with random
all-to-all interactions (the SYK models). The high temperature expansion and
exact diagonalization of the $N$-site fermion model are used to compute the
entropy density: our results are consistent with the numerical solution of
$N=\infty$ saddle point equations, and the presence of a non-zero entropy
density in the limit of vanishing temperature. The exact diagonalization
results for the fermion Green's function also appear to converge well to the
$N=\infty$ solution. For the hard-core boson model, the exact diagonalization
study indicates spin glass order. Some results on the entanglement entropy and
the out-of-time-order correlators are also presented.
