TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.7.6.081
TI  - Topological order in matrix Ising models
PY  - 2019/12/19
UR  - https://www.scipost.org/SciPostPhys.7.6.081
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 7
IS  - 6
SP  - 081
A1  - Hartnoll, Sean A.
AU  - Mazenc, Edward
AU  - Shi, Zhengyan Darius
AB  - 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 [1] 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.
ER  -

@Article{10.21468/SciPostPhys.7.6.081,
	title={{Topological order in matrix Ising models}},
	author={Sean A. Hartnoll and Edward A. Mazenc and Zhengyan D. Shi},
	journal={SciPost Phys.},
	volume={7},
	pages={081},
	year={2019},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.7.6.081},
	url={https://scipost.org/10.21468/SciPostPhys.7.6.081},
}