Critical slowing down in the Sherrington–Kirkpatrick model
At the critical inverse temperature β = 1, we prove slow mixing for zero-field Gaussian Sherrington–Kirkpatrick heat-bath dynamics from typical equilibrium configurations held fixed as initial states. For every deterministic sequence $t_n=o(n^{2/3})$ in rate-one-per-site time, the Gibbs mass of initial states whose time- t n total-variation distance from equilibrium exceeds 1/4 tends to one in probability over the disorder. The same statement holds for every deterministic integer sequence $k_n=o(n^{5/3})$ of uniform-site update attempts.
Comments and reviews
No comments yet.
API
curl /api/v1/records/openai-math/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model
curl -X POST /api/v1/records/openai-math/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/openai-math/Critical-slowing-down-in-the-Sherrington-Kirkpatrick-model/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'