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O(N) rotor model in the large-N limit and the quantum spherical model on graphs

Nikita Titov* and Andrea Trombettoni†

  • *Contact author: nikita.titov@units.it
  • †Contact author: atrombettoni@units.it
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Phys. Rev. B 113, 174209 – Published 21 May, 2026

DOI: https://doi.org/10.1103/k7yv-xjt9

Abstract

We show that the large-n limit of the O(n) quantum rotor model defined on a general graph has the same critical behavior as the corresponding quantum spherical model and that the critical exponents depend solely on the spectral dimension ds of the graph. To this end, we employ a classical to quantum mapping and use known results for the large-n limit of the classical O(n) model on graphs. Away from the critical point, we discuss the interplay between the Laplacian and the Adjacency matrix in the whole parameter plane of the quantum Hamiltonian. These results allow us to paint the full picture of the O(n) quantum rotor model on graphs in the large-n limit.

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Phys. Rev. B 113, 174209– Published 21 May, 2026
  • Received 26 January 2026
  • Accepted 17 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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