A Renormalisation Group Map for Short- and Long-ranged Weakly Coupled |φ|⁴ Models in d ≥ 4 at and Above the Critical Point

2025/11/05 by Jiwoon Park, Park, Jiwoon
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum many-body systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2511.03495

openalex publication_date 2025/11/05 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/30

Abstract

In this article, we construct and analyse a renormalisation group (RG) map for the weakly coupled n-component |φ|⁴ model under periodic boundary conditions in dimension d ≥ 4. Both short-range and long-range interactions with upper critical dimension four are considered. This extends and refines the RG map constructed by Bauerschmidt, Brydges and Slade for the short-range model at d=4. This extension opens the door to establishing the exact decay rate of correlation functions of all of the models discussed. Furthermore, incorporating a large-field decay estimate and comparing with the finite-size scaling results of Michta, Park, and Slade, our analysis provides strong evidence for the emergence of a plateau in systems of finite volume with periodic boundary conditions.

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