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
The continuum scaling limit of the Ising model in d dimensions at theÌýcritical temperatureÌýwhose magnetic field properly scales to zero with lattice spacing isÌý(or should be) aÌýnon-Gaussian generalized random field Phi for d = 2 (and d = 3). ThisÌýfield is (or should be) Ìýrelated to arelativistic quantum field theoryÌýwith one time and d-1Ìýspace coordinates, and no particles of mass below some m_1>0. ÌýTo help study 30 year old conjectures/predictions of ZamolodchikovÌýabout masses Ìým_2, m_3, ... for d=2, we studyÌýa further scaling limit of Phi which yields a stationary Gaussian process X(t) in the timeÌýcoordinate t. ÌýThe covariance function of the X process contains information about the spectrum of particle masses.
(Talk based on joint work with Federico Camia and JianpingÌýJiang, arXiv:1910.12742).
Ìý