2024/12/04 by A. El Alaoui, Alaoui, Ahmed El · 5 citations
Computer Science · Physics and Astronomy · Mathematics · #Topological and Geometric Data Analysis #Theoretical and Computational Physics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2412.03511
We show that in the Ising pure p-spin model of spin glasses, shattering takes place at all inverse temperatures β∈ (√((2 log p)/p), √(2log 2)) when p is sufficiently large as a function of β. Of special interest is the lower boundary of this interval which matches the large p asymptotics of the inverse temperature marking the hypothetical dynamical transition predicted in statistical physics. We show this as a consequence of a `soft' version of the overlap gap property which asserts the existence of a distance gap of points of typical energy from a typical sample from the Gibbs measure. We further show that this latter property implies that stable algorithms seeking to return a point of at least typical energy are confined to an exponentially rare subset of that super-level set, provided that their success probability is not vanishingly small.