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 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 model; its size is logarithmic in the size of the original model.
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