PDE and mathematical physics · Oct 6, 2026
Critical SK autocorrelation processes and dynamics across the temperature transition
For zero-field Gaussian SK heat-bath dynamics with rate-one updates per spin, proves worst-start cutoff on the scale for fixed , mixing time at β = 1, and stretched-exponential mixing from a Gibbs-sampled fixed starting configuration for β > 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.
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