Order-parameter profiles and casimir amplitudes in critical slabs

A critical phase confined between two parallel plates, with symmetry-breaking fields hi and hz acting on each plate, is considered for (i) h(1)h(2) > 0 (denoted nb = ++) and (ii) h(1)h(2) < 0 (ab = +-). Using local-functional methods, we calculate order-parameter scaling functions Psi(ab)(x) and Casimir amplitudes A(ab), for general dimension d. At d = 2, our Psi(++)(x) almost coincides with exact conformal predictions. For the Ising universality class, we obtain expansions for A(ab) in epsilon = 4 - d down arrow 0 in excellent agreement with those obtained from field theory and, in d = 3, new results are presented for A(ab) and Psi(ab)(x). [S0031-9007(98)07753-9].