The truncated correlations of the Ising model in any dimension decay exponentially fast at all but the critical temperature

Abstract

The truncated two-point function of the nearest-neighbor ferromagnetic Ising model on ${\mathbb{Z}}^d$ ($d\ge 3$) in its pure phases is proven to decays exponentially fast throughout the ordered regime ($T<T_c$). Together with known results, this implies that the exponential clustering property holds throughout the model's phase diagram except for the critical point: $(T,h)=(T_c,0)$.

This paper has been withdrawn by the authors due to an error in the proof

Cited by in corpus (1)

• Stein's method for positively associated random variables with applications to the Ising and voter models, bond percolation, and contact process