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

@article{Klausen2022MassSO,
  title={Mass Scaling of the Near-Critical 2D Ising Model Using Random Currents},
  author={Frederik Ravn Klausen and Aran Raoufi},
  journal={Journal of Statistical Physics},
  year={2022}
}
We examine the Ising model at its critical temperature with an external magnetic field ha 15 8 on aZ for a, h > 0. A new proof of exponential decay of the truncated two-point correlation functions is presented. It is proven that the mass (inverse correlation length) is of the order of h 8 15 in the limit h → 0. This was previously proven with CLE-methods in [1]. Our new proof uses instead the random current representation of the Ising model and its backbone exploration. The method further… 
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