A Gaussian process related to the mass spectrum of the near-critical Ising model
I'll discuss joint work with Federico Camia and Jianping Jiang (arXiv:1910.12742). The continuum scaling limit of the Ising model in d dimensions at the critical temperature whose magnetic field properly scales to zero with lattice spacing is (or should be) a non-Gaussian generalized random field Phi for d = 2 (and d = 3). This field is (or should be) related to a relativistic quantum field theory with one time and d-1 space coordinates and no particles of mass below some m_1>0. To help study 30 year old conjectures/predictions of Zamolodchikov about masses m_2, m_3, ... for d=2, we study a further scaling limit of Phi which yields a stationary Gaussian process X(t) in the time coordinate t. The covariance function of the X process contains information about the spectrum of particle masses.