Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem.

@article{Galvani2021MagnetizationPA,
  title={Magnetization profiles at the upper critical dimension as solutions of the integer Yamabe problem.},
  author={Alessandro Galvani and Giacomo Gori and Andrea Trombettoni},
  journal={Physical review. E},
  year={2021},
  volume={104 2-1},
  pages={
          024138
        }
}
We study the connection between the magnetization profiles of models described by a scalar field with marginal interaction term in a bounded domain and the solutions of the so-called Yamabe problem in the same domain, which amounts to finding a metric having constant curvature. Taking the slab as a reference domain, we first study the magnetization profiles at the upper critical dimensions d=3, 4, 6 for different (scale-invariant) boundary conditions. By studying the saddle-point equations for… 

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