Does the SYK model have a spin glass phase?

TL;DR

This paper investigates whether the Sachdev-Ye-Kitaev (SYK) model exhibits a spin glass phase, concluding it does not, based on analytical and numerical analyses of eigenvalue statistics and ground state energy distribution.

Contribution

The paper provides the first comprehensive analysis combining analytical limits and numerical simulations to determine the absence of a spin glass phase in the SYK model.

Findings

SYK model has no spin glass phase.

Eigenvalue statistics support the absence of spin glass behavior.

Ground state energy distribution is Gaussian.

Abstract

We argue that the Sachdev-Ye-Kitaev model has no spin glass phase, based on calculations involving both the nearly-conformal limit and the strongly-coupled Schwarzian limit of the model. This conclusion is supported by numerical computations of eigenvalue statistics with up to 46 Majorana fermions. In addition, we find numerically that the distribution of the ground state energy is Gaussian.