A note on Ursell functions for the Blume-Capel model

Source abstract

We study the sign structure of Ursell functions in the Blume--Capel model. For $Δ\le \log 2$, we give a short proof of the alternating sign property using an Ising representation. We then construct counterexamples for every $Δ> \log 2$, showing that the condition $Δ\le \log 2$ is sharp.