Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations

TL;DR

This paper introduces a new non-equilibrium Monte Carlo method to accurately compute the Casimir amplitude in three-dimensional critical $ ext{O}(N)$ models, providing insights into fluctuation-induced forces at criticality.

Contribution

The paper develops a novel non-equilibrium Monte Carlo algorithm to precisely determine the Casimir amplitude in critical $ ext{O}(N)$ models, advancing numerical techniques in statistical physics.

Findings

High-precision numerical estimates of the Casimir amplitude

Comparison with large-$N$ expansion results

Agreement with conformal bootstrap predictions

Abstract

$\mathrm{O}(N)$ 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 novel non-equilibrium Monte Carlo algorithm, and compare our findings with results obtained from large-$N$ expansions and from the conformal bootstrap.