Large N matrices from a nonlocal spin system

Dionysios Anninos, Sean A. Hartnoll*, Liza Huijse, Victoria L. Martin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Article number195009
JournalClassical and Quantum Gravity
Issue number19
Publication statusPublished - 9 Sept 2015

Bibliographical note

Publisher Copyright:
© 2015 IOP Publishing Ltd.

Other keywords

  • large N
  • matrix models
  • spin systems


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