Abstract: We discuss exponential decay of truncated correlation functions for the two dimensional Ising model in a magnetic field at the critical temperature. The critical exponent corresponding to the scaling of the correlation length in the limit of small fields has been known to be 8/15 for almost 50 years by physicists. Recently, the result was rigorously proven by Camia-Jiang-Newmann using the conformal loop ensemble. We will discuss a new proof using the random current and random cluster graphical representations of the lsing model without using the scaling limit. This is the content of the preprint: https://arxiv.org/abs/2105.13673.
A conjecture in physics related to the existence of additional massive modes will be mentioned.