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

Federico Camia; Jianping Jiang; Charles M. Newman

doi:10.1007/s10955-020-02560-w

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

Federico Camia, Jianping Jiang^*, Charles M. Newman

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

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
Pages (from-to)	885-900
Number of pages	16
Journal	Journal of Statistical Physics
Volume	179
Issue number	4
DOIs	https://doi.org/10.1007/s10955-020-02560-w
Publication status	Published - 20 May 2020

Funding

The research of CMN was supported in part by US-NSF Grant DMS-1507019 and that of JJ by STCSM Grant 17YF1413300. The authors thank Tom Spencer for some useful discussions related to this work.

Funders	Funder number
US-NSF	DMS-1507019
Science and Technology Commission of Shanghai Municipality	17YF1413300
Science and Technology Commission of Shanghai Municipality

Keywords

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

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10.1007/s10955-020-02560-w

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title = "A Gaussian Process Related to the Mass Spectrum of the Near-Critical Ising Model",

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.",

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T1 - A Gaussian Process Related to the Mass Spectrum of the Near-Critical Ising Model

AU - Camia, Federico

AU - Jiang, Jianping

AU - Newman, Charles M.

PY - 2020/5/20

Y1 - 2020/5/20

N2 - 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.

AB - 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.

KW - Gaussian process

KW - Ising model

KW - Magnetization field

KW - Mass spectrum

KW - Near-critical

KW - Quantum field theory

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

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