A Gaussian process related to the mass spectrum of the near-critical Ising model

A Gaussian process related to the mass spectrum of the near-critical Ising model

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Charles Newman, Courant Institute
Jadwin Hall 343

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 arelativistic 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.

(Talk based on joint work with Federico Camia and Jianping Jiang, arXiv:1910.12742).