Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents

We examine the Ising model at its critical temperature with an external magnetic field $$h a^{\frac{15}{8}}$$ on $$a\mathbb {Z}^2$$ for $$a,h >0$$ . A new proof of exponential decay truncated two-point correlation functions is presented. It proven that mass (inverse length) order $$h^\frac{8}{15}$$ in limit \rightarrow 0$$ This was previously CLE-methods Camia et al. (Commun Pure Appl Math 73(7):1371–405, 2020). Our uses instead random current representation and backbone exploration. The method further relies recent couplings to cluster (Aizenman Invent 216:661–743, 2018) as well a near-critical RSW-result (Duminil-Copin Manolescu Planar Random-Cluster Model: Scaling Relations,