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:
- 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.
- 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)