Signs of the Ising model Ursell functions (Q1086260)

It is proved that the Ursell functions \(U_{2k}\) of the Ising model have the conjectured signs: \((-1)^{k+1}U_{2k}\geq 0\). The proof is based on \textit{M. Aizenman}'s [Commun. Math. Phys. 86, 1-48 (1982; Zbl 0533.58034)] random current representation and combinatorics.