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

Year: 2024

Type: preprint

Abstract: We consider a class of non-linear supersymmetric hyperbolic sigma models with long-range interactions on boxes in $\mathbb{Z}^d$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2408.08136

Authors: Disertori, Margherita, Merkl, Franz, Rolles, Silke W. W.

Institutions: University of Bonn, Hausdorff Center for Mathematics, Ludwig-Maximilians-Universität München, Technical University of Munich

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Deutsche Forschungsgemeinschaft

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G3617462173, G8847963564

OpenAlex ID: W4406023782

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