OpenAI reports universal critical SK quench autocorrelation limits

For zero-field Sherrington–Kirkpatrick heat-bath dynamics at β=1, stationary and fair-spin quench autocorrelations converge jointly as random functions after multiplying correlations by n^{1/3} and scaling waiting times and lags by n^{2/3}; Gaussian and Rademacher couplings have the same limiting law, and the quench limit relaxes to the stationary limit as waiting time grows.

Curated contributions 1

Understand the problem ↓

OpenAI reports universal critical SK quench autocorrelation limits

  • Mathematics

For zero-field Sherrington–Kirkpatrick heat-bath dynamics at β=1, stationary and fair-spin quench autocorrelations converge jointly as random functions after multiplying correlations by n^{1/3} and scaling waiting times and lags by n^{2/3}; Gaussian and Rademacher couplings have the same limiting law, and the quench limit relaxes to the stationary limit as waiting time grows.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew

Understanding the problem

Read the background

For zero-field Sherrington–Kirkpatrick heat-bath dynamics at β=1, stationary and fair-spin quench autocorrelations converge jointly as random functions after multiplying correlations by n^{1/3} and scaling waiting times and lags by n^{2/3}; Gaussian and Rademacher couplings have the same limiting law, and the quench limit relaxes to the stationary limit as waiting time grows.

Why it matters

If correct, identifies a common random finite-size critical relaxation process for two coupling laws.

What counts as progress

Do critical SK quench autocorrelations have the same scaled random limit for Gaussian and Rademacher couplings?

Website timeline

Publication dates and editorial changes.