{"id":"hexagon/2610.00241","pdf":"https://hexagonmath.org/pdf/2610.00241v1","url":"https://hexagonmath.org/abs/2610.00241v1","tags":["math-ph","msc:05C60","msc:05C35","msc:82B20","antiferromagnetic models","graph homomorphisms","partition functions"],"score":0,"title":"A six-spin obstruction to antiferromagnetic biclique maximization","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Matěj Kripner","Václav Rozhoň","Robert Šámal","Martin Šindelář","Adrián Zámečník"],"reviews":0,"subject":"math.CO","summary":"Sah, Sawhney, Stoner and Zhao conjectured that for every spin model whose interaction matrix has exactly one positive eigenvalue, the partition function of any graph is at most a product of biclique partition functions determined by its edge degrees. We disprove this conjecture with a strictly positive six-spin model on a triangle with three pendant edges; the violation persists on an open set of nonsingular models. The mechanism is a negative mixed covariance trace at vertices of degrees two, three and four: the triangle contributes a favourable cubic term, whereas all biclique corrections…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Bolzano"],"discussed":0,"published":"2026-10-14","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}