2024/01/16 by David Belius, Belius, David, Francesco Concetti +3 · 2 citations
Materials Science · Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nanocluster Synthesis and Applications #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2401.08529
openalex publication_date 2024/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the computation of the TAP complexity, originally carried out by Bray and Moore, a fundamental step is to calculate the determinant of a random Hessian. As the replica method does not give a clear prescription, physicists debated how to perform this computation and its consequences on the TAP complexity for a long time. In this paper we prove the original Bray and Moore formula for the behaviour of the determinant at exponential scale to be correct, and compute an important prefactor coming from a small outlier in the spectrum.