F. Camia: Perturbing the critical Ising model

Abstract: We consider the effect of an external magnetic field on the scaling limit of the Ising model at the critical temperature in different dimensions and with different boundary conditions. More precisely:

  1. In two dimensions, we show that the near-critical scaling limit of the model with an external magnetic field leads to a field theory with a mass gap in the energy-momentum spectrum, and discuss the mass spectrum of the theory.
  2. In high dimensions and with free boundary conditions, we discuss the surprising result that the same type of perturbation does not lead to a mass gap.

(Based on joint work by F. Camia, J. Jiang and C.M. Newman)

arXiv: 2111.05146


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