Sean A. Hartnoll, Edward A. Mazenc, Zhengyan D. Shi
SciPost Phys. 7, 081 (2019) ·
published 19 December 2019
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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.
