A 2D disordered O(N) sigma model at large N exhibits a low-temperature spin glass phase with finite Edwards-Anderson parameter and approximate scaling in the dynamical two-point function.
Higher Dimensional Generalizations of the SYK Model
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abstract
We discuss a 1+1 dimensional generalization of the Sachdev-Ye-Kitaev model. The model contains $N$ Majorana fermions at each lattice site with a nearest-neighbour hopping term. The SYK random interaction is restricted to low momentum fermions of definite chirality within each lattice site. This gives rise to an ordinary 1+1 field theory above some energy scale and a low energy SYK-like behavior. We exhibit a class of low-pass filters which give rise to a rich variety of hyperscaling behaviour in the IR. We also discuss another set of generalizations which describes probing an SYK system with an external fermion, together with the new scaling behavior they exhibit in the IR.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Numerical study of the SYK-q spin model finds rapid entanglement growth to Haar-random saturation, a universal Rényi-1/2 mutual information vs negativity relation at minimal q, and Page-curve behavior in negativity under unequal partitions.
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The two-dimensional disordered $O(N)$ sigma model
A 2D disordered O(N) sigma model at large N exhibits a low-temperature spin glass phase with finite Edwards-Anderson parameter and approximate scaling in the dynamical two-point function.
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Information scrambling in all-to-all interacting models
Numerical study of the SYK-q spin model finds rapid entanglement growth to Haar-random saturation, a universal Rényi-1/2 mutual information vs negativity relation at minimal q, and Page-curve behavior in negativity under unequal partitions.