## 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 language | English |
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Pages (from-to) | 885-900 |

Number of pages | 16 |

Journal | Journal of Statistical Physics |

Volume | 179 |

Issue number | 4 |

DOIs | |

Publication status | Published - 20 May 2020 |

## Keywords

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