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arXiv · 1412.1092

Large N matrices from a nonlocal spin system

Dionysios Anninos·Sean A. Hartnoll·Liza Huijse·Victoria L. Martin
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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.

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Dionysios Anninos, Sean A. Hartnoll, Liza Huijse, Victoria L. Martin. 2014-12-02. Large N matrices from a nonlocal spin system. https://doi.org/10.1088/0264-9381%2F32%2F19%2F195009

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