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arXiv · 2606.27925

The two-dimensional disordered $O(N)$ sigma model

Martí Berenguer·Felix M. Haehl·Elisa Tabor
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Abstract

We introduce a two-dimensional $O(N)$ nonlinear sigma model with random Gaussian $p$-body interactions. The model combines the structure of a two-dimensional bosonic SYK-type quantum field theory with the stabilizing spherical constraint of the nonlinear sigma model. At large $N$ we derive the Schwinger-Dyson equations on a torus and analyze the solutions using both analytical approximations and numerical methods. We find a phase diagram qualitatively similar to that of the one-dimensional quantum spherical $p$-spin model, including a low-temperature transition to a spin glass phase. This phase is characterized by a finite Edwards-Anderson order parameter, while the dynamical part of the two-point function displays an approximate scaling regime. These results provide a tractable setting for studying approximate conformal behavior and glassy physics in a two-dimensional relativistic field theory with disorder.

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Martí Berenguer, Felix M. Haehl, Elisa Tabor. 2026-06-26. The two-dimensional disordered $O(N)$ sigma model. https://arxiv.org/abs/2606.27925

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