Topological order in matrix Ising models

Journal Article · Wed Dec 18 23:00:00 EST 2019 · SciPost Physics

DOI:https://doi.org/10.21468/SciPostPhys.7.6.081· OSTI ID:1579979

Hartnoll, Sean ^[1]; Mazenc, Edward ^[1]; Shi, Zhengyan ^[1]

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1. Stanford University

We study a family of models for an N_1 \times N_2 $N_1\times N_2$ matrix worth of Ising spins S_{aB} $S_{aB}$ . In the large N_i $N_i$ limit we show that the spins soften, so that the partition function is described by a bosonic matrix integral with a single ‘spherical’ constraint. In this way we generalize the results of to a wide class of Ising Hamiltonians with O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) $O(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z})$ symmetry. The models can undergo topological large N $N$ phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} $S_{aB}$ becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0018134
• OSTI ID: 1579979
• Alternate ID(s): OSTI ID: 1803258
• Journal Information: SciPost Physics, Journal Name: SciPost Physics Journal Issue: 6 Vol. 7; ISSN 2542-4653
• Publisher: Stichting SciPost
• Country of Publication: Netherlands
• Language: English