Critical Casimir amplitudes for n-component image models with image-symmetry breaking quadratic boundary terms Original Research Article

Euclidean n-component image theories whose Hamiltonians are image symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry image. The boundary terms imply the Robin boundary conditions image at the boundary planes image at image and image at image. Particular attention is paid to the cases in which image of the n variables image associated with plane image take the special value image corresponding to critical enhancement while the remaining ones are larger and hence subcritically enhanced. Under these conditions, the semi-infinite system with boundary plane image has a multicritical surface–bulk point, called image-special, at which an image symmetric critical surface phase coexists with the image symmetric bulk phase, provided d is sufficiently large. The L-dependent part of the reduced free energy per cross-section area behaves asymptotically as image as image at the bulk critical point. The Casimir amplitudes image are determined for small image in the general case where image components image are critically enhanced at both boundary planes, image components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining image components satisfy asymptotic Dirichlet boundary conditions at both image. Whenever image, the corresponding small-ϵ expansions involve, besides integer powers of ϵ, also fractional powers image with image modulo powers of logarithms. Results to order image are given for general values of image, image, and image. These are used to estimate the Casimir amplitudes image of the three-dimensional Heisenberg systems with surface spin anisotropies for the cases with image, image, and image.