1212.2647 (Pawel Jakubczyk et al.)

Thermal Casimir forces for the O(N)-models from functional
renormalization    [PDF]

Pawel Jakubczyk, Marek Napiorkowski

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 thermal Casimir forces acting between the slab boundaries at criticality. The applied truncation of the exact functional RG flow equation (leading order in the derivative expansion) neglects renormalization of the momentum dependencies in the propagator, but 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.

View original: http://arxiv.org/abs/1212.2647