A six-spin obstruction to antiferromagnetic biclique maximization
Source: hexagonmath.org/abs/2610.00241v1
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…
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