Topological order in matrix Ising models
Abstract
We study a family of models for an N_1 \times N_2 matrix worth of Ising spins S_{aB} . In the large 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}) symmetry. The models can undergo topological large N phase transitions in which the thermal expectation value of the distribution of singular values of the matrix S_{aB} becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.
- Authors:
-
- Stanford University
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1579979
- Grant/Contract Number:
- SC0018134
- Resource Type:
- Published Article
- Journal Name:
- SciPost Physics Proceedings
- Additional Journal Information:
- Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 6; Journal ID: ISSN 2542-4653
- Publisher:
- Stichting SciPost
- Country of Publication:
- Netherlands
- Language:
- English
Citation Formats
Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Topological order in matrix Ising models. Netherlands: N. p., 2019.
Web. doi:10.21468/SciPostPhys.7.6.081.
Hartnoll, Sean, Mazenc, Edward, & Shi, Zhengyan. Topological order in matrix Ising models. Netherlands. doi:https://doi.org/10.21468/SciPostPhys.7.6.081
Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Thu .
"Topological order in matrix Ising models". Netherlands. doi:https://doi.org/10.21468/SciPostPhys.7.6.081.
@article{osti_1579979,
title = {Topological order in matrix Ising models},
author = {Hartnoll, Sean and Mazenc, Edward and Shi, Zhengyan},
abstractNote = {We study a family of models for an N_1 \times N_2 N 1 × N 2 matrix worth of Ising spins S_{aB} S a B . 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 , ℤ ) × O ( N 2 , 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 a B becomes disconnected. This topological transition competes with low temperature glassy and magnetically ordered phases.},
doi = {10.21468/SciPostPhys.7.6.081},
journal = {SciPost Physics Proceedings},
number = 6,
volume = 7,
place = {Netherlands},
year = {2019},
month = {12}
}
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DOI: https://doi.org/10.21468/SciPostPhys.7.6.081
DOI: https://doi.org/10.21468/SciPostPhys.7.6.081
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