Order-parameter profiles and casimir amplitudes in critical slabs

Abstract

A critical phase confined between two parallel plates, with symmetry-breaking fields h1 and h2 acting on each plate, is considered for (i) h1h2 > 0 (denoted ab=++) and (ii) h1h2 < 0 (ab=+-). Using local-functional methods, we calculate order-parameter scaling functions Ψab(x) and Casimir amplitudes Aab, for general dimension d. At d = 2, our Ψ++(x) almost coincides with exact conformal predictions. For the Ising universality class, we obtain expansions for Aab in ε = 4 - d ↓ 0 in excellent agreement with those obtained from field theory and, in d=3, new results are presented for Aab and Ψab(x). © 1998 The American Physical Society.