The non-linear supersymmetric hyperbolic sigma model on a complete graph with hierarchical interactions

2021/11/16 by Margherita Disertori, Disertori, Margherita, Franz Merkl +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary: 82B20 #Probability (math.PR) #Quantum Chromodynamics and Particle Interactions #Secondary: 60G60

paper · pdf · doi:10.48550/arxiv.2111.08293

openalex publication_date 2021/11/16 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We study the non-linear supersymmetric hyperbolic sigma model H^2|2 on a complete graph with hierarchical interactions. For interactions which do not decrease too fast in the hierarchical distance, we prove tightness of certain spin variables in horospherical coordinates, uniformly in the pinning and in the size of the graph. The proof relies on a reduction to an effective H^2|2 model; its size is logarithmic in the size of the original model.

Cited by

• VRJP recurrence and fractional-moment decay for the \(H^2|2\) model's effective field on the hierarchical lattice

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