Casimir effect in critical O(<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>N</mi></mrow></math>) models from nonequilibrium Monte Carlo simulations

Andrea Bulgarelli; Michele Caselle; Alessandro Nada; Marco Panero

doi:10.1103/lcvl-dgv4

Casimir effect in critical O( $N$ ) models from nonequilibrium Monte Carlo simulations

Andrea Bulgarelli ^1,2,3,*, Michele Caselle ^1,2, Alessandro Nada ^1,2, and Marco Panero ^1,2,4

¹Department of Physics, University of Turin, Via Pietro Giuria 1, I-10125 Turin, Italy
²INFN, Turin division, Via Pietro Giuria 1, I-10125 Turin, Italy
³Transdisciplinary Research Area “Building Blocks of Matter and Fundamental Interactions” (TRA Matter) and Helmholtz Institute for Radiation and Nuclear Physics (HISKP), University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
⁴Department of Physics and Helsinki Institute of Physics, PL 64, University of Helsinki, FIN-00014 Helsinki, Finland

^*Contact author: andrea.bulgarelli@unito.it

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Phys. Rev. E 112, 064126 – Published 19 December, 2025

DOI: https://doi.org/10.1103/lcvl-dgv4

Abstract

$O (N)$ vector models in three dimensions, when defined in a geometry with a compact direction and tuned to criticality, exhibit long-range fluctuations which induce a Casimir effect. The strength of the resulting interaction is encoded in the excess free-energy density, which depends on a universal coefficient: the Casimir amplitude. We present a high-precision numerical calculation of the latter by means of a nonequilibrium Monte Carlo algorithm and compare our findings with results obtained from large- $N$ expansions and from the conformal bootstrap.

Physical Review E

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Casimir effect in critical O( $N$ ) models from nonequilibrium Monte Carlo simulations

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Casimir effect in critical O(N) models from nonequilibrium Monte Carlo simulations

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Casimir effect in critical O( $N$ ) models from nonequilibrium Monte Carlo simulations