Does the SYK model have a spin glass phase?
Guy Gur-Ari (Department of Physics, Stanford University, Stanford, CA, U.S.A., School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, U.S.A., Google LLC, Menlo Park, U.S.A.); Raghu Mahajan (Department of Physics, Princeton University, Princeton, NJ, U.S.A., School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, U.S.A.); Abolhassan Vaezi (Department of Physics, Stanford University, Stanford, CA, U.S.A.)
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.
