The Gaussian process for particle masses in the near-critical Ising\n model

2021/11/09 by Federico Camia, Jianping Jiang, Camia, Federico +3 · 1 citation
Mathematics · Physics and Astronomy · #81T40 #82B20 #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Primary: 60K35 #Probability (math.PR) #Secondary: 82B27 #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2111.05134

openalex publication_date 2021/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the construction of a stationary Gaussian process X(t) starting\nfrom the near-critical continuum scaling limit \Φ^h of the Ising\nmagnetization and its relation to the mass spectrum of the relativistic quantum\nfield theory associated to \Φ^h. Then for the near-critical Ising model on\na \ℤ² with external field a^15/8 h, we study the renormalized\nmagnetization along a vertical line (with horizontal coordinate approximately\nt) and prove that the limit as a downarrow 0 is the same Gaussian process\nX(t). We also explore the possible extension of this approach to dimensions\nd > 2.\n

Citations

• Planar Ising magnetization field II. Properties of the critical and\n near-critical scaling limits

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