2026-07-22T12:15:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:22689 2026-04-17T05:32:20Z ddc:004 open_access

Hardness of Sampling for the Anti-Ferromagnetic Ising Model on Random Graphs Huang, Neng Perkins, Will Potechin, Aaron Random graph spin glass sampling algorithm We prove a hardness of sampling result for the anti-ferromagnetic Ising model on random graphs of average degree d for large constant d, proving that when the normalized inverse temperature satisfies β > 1 (asymptotically corresponding to the condensation threshold), then w.h.p. over the random graph there is no stable sampling algorithm that can output a sample close in W₂ distance to the Gibbs measure. The results also apply to a fixed-magnetization version of the model, showing that there are no stable sampling algorithms for low but positive temperature max and min bisection distributions. These results show a gap in the tractability of search and sampling problems: while there are efficient algorithms to find near optimizers, stable sampling algorithms cannot access the Gibbs distribution concentrated on such solutions. Our techniques involve extensions of the interpolation technique relating behavior of the mean field Sherrington-Kirkpatrick model to behavior of Ising models on random graphs of average degree d for large d. While previous interpolation arguments compared the free energies of the two models, our argument compares the average energies and average overlaps in the two models. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Neng Huang and Will Perkins and Aaron Potechin 2025 Is Part Of LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2025.61 urn:nbn:de:0030-drops-226899 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.61 eng https://creativecommons.org/licenses/by/4.0/legalcode