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Title: Topological order in matrix Ising models

Abstract

We study a family of models for anN_1 \times N_2 N 1 × N 2 matrix worth of Ising spinsS_{aB} S a B .In the largeN_i N i limit we show that the spins soften, so that the partition function isdescribed by a bosonic matrix integral with a single ‘spherical’constraint. In this way we generalize the results of to a wide class ofIsing Hamiltonians withO(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z}) O ( N 1 , Z ) × O ( N 2 , Z ) symmetry. The models can undergo topological largeN N phase transitions in which the thermal expectation value of thedistribution of singular values of the matrixS_{aB} S a B becomes disconnected. This topological transition competes with lowtemperature glassy and magnetically ordered phases.

Authors:
 [1];  [1];  [1]
  1. Stanford Univ., CA (United States). Dept. of Physics
Publication Date:
Research Org.:
Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1579979
Alternate Identifier(s):
OSTI ID: 1803258
Grant/Contract Number:  
SC0018134
Resource Type:
Published Article
Journal Name:
SciPost Physics
Additional Journal Information:
Journal Volume: 7; Journal Issue: 6; Journal ID: ISSN 2542-4653
Publisher:
SciPost Foundation
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics

Citation Formats

Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Topological order in matrix Ising models. United States: N. p., 2019. Web. doi:10.21468/scipostphys.7.6.081.
Hartnoll, Sean, Mazenc, Edward, & Shi, Zhengyan. Topological order in matrix Ising models. United States. https://doi.org/10.21468/scipostphys.7.6.081
Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Thu . "Topological order in matrix Ising models". United States. 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 anN_1 \times N_2N1×N2matrix worth of Ising spinsS_{aB}SaB.In the largeN_iNilimit we show that the spins soften, so that the partition function isdescribed by a bosonic matrix integral with a single ‘spherical’constraint. In this way we generalize the results of to a wide class ofIsing Hamiltonians withO(N_1,\mathbb{Z})\times O(N_2,\mathbb{Z})O(N1,Z)×O(N2,Z)symmetry. The models can undergo topological largeNNphase transitions in which the thermal expectation value of thedistribution of singular values of the matrixS_{aB}SaBbecomes disconnected. This topological transition competes with lowtemperature glassy and magnetically ordered phases.},
doi = {10.21468/scipostphys.7.6.081},
journal = {SciPost Physics},
number = 6,
volume = 7,
place = {United States},
year = {2019},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.21468/scipostphys.7.6.081

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Cited by: 2 works
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