Abstract in English:

Systems described by an O(n) symmetrical 4 Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes Bj, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions n=cj. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form fresD(c1LΦ/ν,c2LΦ/ν)/ Ld-1 when d<4, where ci are scaling fields associated with the variables ci and Φ is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c1,c2) at d=4- dimensions are presented. These show that (i)the Casimir force can have either sign, depending on c1 and c2, and (ii)for appropriate choices of the enhancements cj, crossovers from attraction to repulsion and vice versa occur as L increases. © 2008 The American Physical Society.