Extension of the Pfaffian asymptotics to Simon–Griffiths spin systems

Let a similar finite-range, ferromagnetic, translation-invariant and reflection-invariant system be obtained by replacing the Ising spins in Theorem 1 with spin variables in the Simon–Griffiths class, and let $\beta_c$ denote its correspondingly adjusted critical inverse temperature. Simon–Griffiths extension conjecture. The conclusion of the Pfaffian asymptotic theorem holds for this system: for boundary points $x_1,\ldots,x_{2n}$ whose mutual distances tend to infinity, the $2n$-point spin correlation is asymptotic to the Pfaffian built from the corresponding two-point correlations, with relative error tending to zero. The conjecture proposes that the stochastic-geometric mechanism behind the Ising result extends beyond Ising spins to the Simon–Griffiths class; no proof or resolution is given here.