Remark: Family 227. The dynamical phase transition in the Sherrington–Kirkpatrick model

For zero-field Gaussian SK heat-bath dynamics with rate-one updates per spin, proves worst-start cutoff on the $\log n$ scale for fixed $0\le \beta <1$, mixing time $n^{2/3+o(1)}$ at $\beta =1$, and stretched-exponential mixing from a Gibbs-sampled fixed starting configuration for $\beta >1$, in probability over disorder. At criticality, rescaled stationary and quench autocorrelation processes have universal random limits for Gaussian and Rademacher disorder; the quench limit relaxes to the stationary limit.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.