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We consider the Ising model at its critical temperature with externalmagnetic field $ha^{15/8}$ on the square lattice with lattice spacing $a$. Weshow that the truncated two-point function in this model decays exponentiallywith a rate independent of $a$. As a consequence, we show exponential decay inthe near-critical scaling limit Euclidean magnetization field. For the latticemodel with $a=1$, the mass (inverse correlation length) is of order $h^{8/15}$as $h\downarrow 0$; for the Euclidean field, it equals exactly $Ch^{8/15}$ forsome $C$. Although there has been much progress in the study of criticalscaling limits, results on near-critical models are far fewer due to the lackof conformal invariance away from the critical point. Our arguments combinelattice and continuum FK representations, including coupled conformal loop andmeasure ensembles, showing that such ensembles can be useful even in the studyof near-critical scaling limits. Thus we provide the first substantialapplication of measure ensembles.

Exponential decay for the near-critical scaling limit of the planar Ising model