High-temperature free-energy fluctuations in the SYK model
Follow the latest progress by email.
The Gaussian q-body Sachdev–Ye–Kitaev (SYK) model describes randomly interacting Majorana fermions. For fixed even q≥4, what is the limiting distribution of N^(q/2−1)(log Z_N−E log Z_N), where Z_N is the partition function? The target takes even N to infinity at a fixed, sufficiently small positive inverse temperature.
Why it matters and what counts as progress
Why it matters: The fluctuation law describes sample-to-sample variation beyond the average free energy in a quantum-disorder model studied in statistical physics and holography.
What counts as progress: Establish the limiting distribution, its nonzero variance and a valid high-temperature range under the stated normalization. A result in this regime does not establish the low-temperature behavior.
How the problem developed
- 4 May 2026 · Free energy limit [1]
David Gamarnik, Francisco Pernice, Alexander Schmidhuber and Alexander Zlokapa Reported rigorous annealed and quenched free-energy limits for the SYK model at sufficiently high but constant temperature.
- 13 Oct 2026 · Central limit theorem [2]
Yoshinori Kamijima, Shuta Nakajima, Ryoichiro Noda and Kôhei Sasaya Proved a high-temperature central limit theorem for centered log partition functions in the Gaussian q-body SYK model, for fixed even q≥4 and sufficiently small inverse temperature; the paper describes Lean formalization of the main arguments.
AI contribution
A Central Limit Theorem for High-Temperature SYK Model
Kamijima, Nakajima, Noda and Sasaya report a nondegenerate Gaussian limit for N^(q/2−1)(log Z_N−E log Z_N) in the Gaussian q-body SYK model, for fixed even q≥4 and sufficiently small nonzero inverse temperature.
Sources
Website timeline
Publication dates and editorial changes.
AI-assisted Gaussian free-energy fluctuations in the high-temperature SYK model