A Gaussian Process Related to the Mass Spectrum of the Near-Critical Ising Model

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Abstract

Let Φ h(x) with x= (t, y) denote the near-critical scaling limit of the planar Ising magnetization field. We take the limit of Φ h as the spatial coordinate y scales to infinity with t fixed and prove that it is a stationary Gaussian process X(t) whose covariance function K(t) is the Laplace transform of a mass spectral measure ρ of the relativistic quantum field theory associated to the Euclidean field Φ h. X and K should provide a useful tool for studying the mass spectrum; e.g., the small distance/time behavior of the covariance functions of Φ h and X(t) shows that ρ is finite but has infinite first moment.

Original languageEnglish (US)
Pages (from-to)885-900
Number of pages16
JournalJournal of Statistical Physics
Volume179
Issue number4
DOIs
StatePublished - May 1 2020

Keywords

  • Gaussian process
  • Ising model
  • Magnetization field
  • Mass spectrum
  • Near-critical
  • Quantum field theory

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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