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Title: Topological order in matrix Ising models

Abstract

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 , ) × O ( N 2 , ) 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.

Authors:
 [1];  [1];  [1]
  1. 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:10.21468/SciPostPhys.7.6.081.
Hartnoll, Sean, Mazenc, Edward, and Shi, Zhengyan. Thu . "Topological order in matrix Ising models". Netherlands. doi: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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.7.6.081

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