  Large N matrices underpin the best understood models of emergent spacetime.
We suggest that large N matrices can themselves be emergent from simple quantum
mechanical spin models with finite dimensional Hilbert spaces. We exhibit the
emergence of large N matrices in a nonlocal statistical physics model of order
N^2 Ising spins. The spin partition function is shown to admit a large N saddle
described by a matrix integral, which we solve. The matrix saddle is dominant
at high temperatures, metastable at intermediate temperatures and ceases to
exist below a critical order one temperature. The matrix saddle is disordered
in a sense we make precise and competes with ordered low energy states. We
verify our analytic results by Monte Carlo simulation of the spin system.

High Energy Physics - Theory