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

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.