## Abstract

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.

Original language | English |
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Article number | 195009 |

Journal | Classical and Quantum Gravity |

Volume | 32 |

Issue number | 19 |

DOIs | |

Publication status | Published - 9 Sept 2015 |

### Bibliographical note

Publisher Copyright:© 2015 IOP Publishing Ltd.

## Other keywords

- large N
- matrix models
- spin systems