2016/12/29 by Yuting Chen, Chen, Yu-Ting
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1612.09250
openalex publication_date 2016/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove universality of the Ghirlanda-Guerra identities and spin distributions in the mixed p-spin models. The assumption for the universality of the identities requires exactly that the coupling constants have zero means and finite variances, and the result applies to the Sherrington-Kirkpatrick model. As an application, we obtain weakly convergent universality of spin distributions in the generic p-spin models under the condition of two matching moments. In particular, certain identities for 3-overlaps and 4-overlaps under the Gaussian disorder follow. Under the stronger mode of total variation convergence, we find that universality of spin distributions in the mixed p-spin models holds if mild dilution of connectivity by the Viana-Bray diluted spin glass Hamiltonians is present and the first three moments of coupling constants in the mixed p-spin Hamiltonians match. These universality results are in stark contrast to the characterization of spin distributions in the undiluted mixed p-spin models, which is known up to now that four matching moments are required in general.