Monte Carlo simulation of Casimir force scaling functions for 3D
Ising and XY models
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Critical Casimir forces arise
in fluctuating media near critical points due to finite size
contributions to the free energy of a system. The critical Casimir force
in a slab of thickness $L$ scales as
$f_Casimir(T,L)=L^-dþeta_Casimir(L/\xi)$
where $þeta(L/\xi)$ is a universal scaling function and $\xi$ is the correlation length.
A new Monte Carlo method is developed to compute the
scaling functions of Casimir forces for lattice models (Ising,
XY).
The method is based on an integration scheme of free energy
differences. Numerical results are presented
for periodic, $++$ and $+-$ boundary conditions (Ising) and periodic and
open boundary conditions (XY). These results are expected to
contribute to the understanding of recent
experiments on critical films of binary mixtures (Ising) and $^4$He (XY),
respectively.