Title:Exponential decay for the near-critical scaling limit of the planar Ising model
Abstract:
We consider the Ising model at its critical temperature with external
magnetic field $ha^{15/8}$ on the square lattice with lattice spacing a.
We show that the truncated two-point function in this model decays
exponentially with a rate independent of a. We also show exponential decay
in the near-critical scaling limit Euclidean magnetization field. For the
lattice model with a=1, the mass (inverse correlation length) is of order
$h^{8/15}$ as $hâ†“ 0$ for the Euclidean field, it equals exactly $C h^{8/15}$
for some C. Our arguments combine lattice and continuum FK representations,
including coupled conformal loop and measure ensembles, showing that such
coupled ensembles can be useful even in the study of near-critical scaling
limits.