English

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

Probability 2021-11-17 v1 Mathematical Physics math.MP

Abstract

We study the non-linear supersymmetric hyperbolic sigma model H22H^{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 H22H^{2|2} model; its size is logarithmic in the size of the original model.

Keywords

Cite

@article{arxiv.2111.08293,
  title  = {The non-linear supersymmetric hyperbolic sigma model on a complete graph with hierarchical interactions},
  author = {Margherita Disertori and Franz Merkl and Silke W. W. Rolles},
  journal= {arXiv preprint arXiv:2111.08293},
  year   = {2021}
}

Comments

24 pages, 3 figures

R2 v1 2026-06-24T07:40:08.952Z