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

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.