A critical phase confined between two parallel plates, with symmetry-breaking fields $h_1$ and $h_2$ acting on each plate, is considered for (i) $h_1{h}_2>0\mathrm{}$ (denoted $ab=++$) and (ii) $h_1{h}_2<0\mathrm{}$ ( $ab=+-$). Using local-functional methods, we calculate order-parameter scaling functions ${\Psi }_{\mathrm{ab}}\left(x\right)$ and Casimir amplitudes $A_{\mathrm{ab}}$, for general dimension $d$. At $d=2\mathrm{}$, our ${\Psi }_{++}\left(x\right)$ almost coincides with exact conformal predictions. For the Ising universality class, we obtain expansions for $A_{\mathrm{ab}}$ in $\epsilon =4-d\downarrow 0$ in excellent agreement with those obtained from field theory and, in $d=3\mathrm{}$, new results are presented for $A_{\mathrm{ab}}$ and ${\Psi }_{\mathrm{ab}}\left(x\right)$.

• Received 7 August 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.4911