English

Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions

Mathematical Physics 2024-08-16 v1 math.MP Probability

Abstract

We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in Zd\mathbb{Z}^d and on a hierarchical lattice. We prove that the random field associated to a marginal in horospherical coordinates has asymptotically arbitrarily small fluctuations for large enough interactions, uniformly in the size of the boxes. This can be viewed as a strong version of spontaneous breaking of the Lorentz boost symmetry.

Keywords

Cite

@article{arxiv.2408.08136,
  title  = {Fluctuations in the non-linear supersymmetric hyperbolic sigma model with long-range interactions},
  author = {Margherita Disertori and Franz Merkl and Silke W. W. Rolles},
  journal= {arXiv preprint arXiv:2408.08136},
  year   = {2024}
}

Comments

27 pages, 2 figures. This manuscripts was obtained by splitting and updating arXiv:2305.07359v1 into this manuscript and arXiv:2305.07359v2

R2 v1 2026-06-28T18:13:45.631Z