Casimir effect in critical O(N) models from nonequilibrium Monte Carlo simulations
Andrea Bulgarelli1,2,3, Michele Caselle1,2, Alessandro Nada1,2
1University of Turin, Department of Physics, Via Pietro Giuria 1, I-10125 Turin, Italy.
Physical Review. E
|January 21, 2026
Summary
Critical O(N) vector models exhibit a Casimir effect due to long-range fluctuations. This study precisely calculates the Casimir amplitude, a key interaction strength, using a nonequilibrium Monte Carlo algorithm.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Quantum Field Theory
Background:
- O(N) vector models in three dimensions with a compact direction exhibit criticality.
- Long-range fluctuations in these systems induce a Casimir effect.
- The Casimir amplitude quantifies the interaction strength via excess free-energy density.
Purpose of the Study:
- To present a high-precision numerical calculation of the Casimir amplitude.
- To compare numerical findings with theoretical predictions from large-N expansions and the conformal bootstrap.
Main Methods:
- Utilized a nonequilibrium Monte Carlo algorithm for numerical calculation.
- Focused on O(N) vector models in three dimensions with a compact direction tuned to criticality.
Main Results:
- Achieved high-precision numerical results for the Casimir amplitude.
- Provided a comparison of numerical findings against large-N expansions and conformal bootstrap predictions.
Conclusions:
- The study offers precise numerical data for the Casimir amplitude in critical O(N) vector models.
- The findings contribute to understanding critical phenomena and the Casimir effect in condensed matter systems.
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