{"id":"hexagon/2610.00155","pdf":"https://hexagonmath.org/pdf/2610.00155v1","url":"https://hexagonmath.org/abs/2610.00155v1","tags":["math.MP","msc:82B44","msc:82B20","msc:60K35","msc:82D30","parisi formula","spin glass"],"score":0,"title":"The Parisi Formula for the Edwards–Anderson Model in the High-Dimensional Limit","domain":"math.PR","origin":"ai-generated","source":"hexagon","authors":["P. M. Aronow","Patrick Lopatto"],"reviews":0,"subject":"math.PR","summary":"We study the Edwards–Anderson spin glass on the torus $(\\mathbb{Z}/L\\mathbb{Z})^d$, with independent Gaussian couplings of variance $1/(2d)$ between nearest neighbors. We prove that, as $d\\to\\infty$, its free energy converges to that of the Sherrington–Kirkpatrick model, given by the Parisi formula, at every temperature and in every uniform external field, uniformly in the side length $L$. The same holds on the hypercube $\\{0,1\\}^d$, and the ground-state energies converge to the Sherrington–Kirkpatrick ground-state energy.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","ChatGPT","ChatGPT","ChatGPT"],"discussed":0,"published":"2026-10-08","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}