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 N2 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.
|Journal||Classical and Quantum Gravity|
|Publication status||Published - 9 Sept 2015|
Bibliographical notePublisher Copyright:
© 2015 IOP Publishing Ltd.
- large N
- matrix models
- spin systems