Critical Casimir forces for O(N) models from functional renormalization

TL;DR

This paper uses functional renormalization group methods to compute critical Casimir forces in O(N) models within slab geometries, achieving results that align well with exact and Monte Carlo data.

Contribution

It introduces a truncation scheme in functional RG that retains arbitrary interaction vertices, enabling accurate computation of Casimir amplitudes across dimensions and N values.

Findings

Excellent agreement with exact results for d=2, N=1

Closer to Monte Carlo results for d=3 than previous RG methods

Wave function renormalization has negligible effect on forces

Abstract

We consider the classical O(N)-symmetric models confined in a d-dimensional slab-like geometry and subject to periodic boundary conditions. Applying the one-particle-irreducible variant of functional renormalization group (RG) we compute the critical Casimir forces acting between the slab boundaries. The applied truncation of the exact functional RG flow equation retains interaction vertices of arbitrary order. We evaluate the critical Casimir amplitudes \Delta_f(d,N) for continuously varying dimensionality between two and three and N = 1,2. Our findings are in very good agreement with exact results for d=2 and N=1. For d=3 our results are closer to Monte Carlo predictions than earlier field-theoretic RG calculations. Inclusion of the wave function renormalization and the corresponding anomalous dimension in the calculation has negligible impact on the computed Casimir forces.