Crossover from Attractive to Repulsive Casimir Forces and Vice Versa

Abstract

Systems described by an O(n) symmetrical ${\varphi }^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes ${\mathfrak{B}}_j,j=1,2$, are investigated as functions of film thickness $L$ for generic symmetry-preserving boundary conditions ${\partial }_n\mathbf{\varphi }={\mathring{c}}_j\mathbf{\varphi }$. The $L$-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form $f_{\text{res}}\approx D(c_1{L}^{\Phi /\nu },c_2{L}^{\Phi /\nu })/L^{d-1}$ when $d<4$, where $c_i$ are scaling fields associated with the variables ${\mathring{c}}_i$, and $\Phi$ is a surface crossover exponent. Explicit two-loop renormalization group results for the function $D({\mathsf{c}}_1,{\mathsf{c}}_2)$ at $d=4-\epsilon$ dimensions are presented. These show that (i) the Casimir force can have either sign, depending on ${\mathsf{c}}_1$ and ${\mathsf{c}}_2$, and (ii) for appropriate choices of the enhancements ${\mathring{c}}_j$, crossovers from attraction to repulsion and vice versa occur as $L$ increases.

4 RevTeX pages, 2 eps figures; minor misprints corrected and 3 references added

References in corpus (2)

• Monte Carlo simulation results for critical Casimir forces
• Thermodynamic Casimir effects involving interacting field theories with zero modes