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Finite-size effects are investigated in the Gaussian model with isotropic andanisotropic short-range interactions in film geometry with nonperiodic boundaryconditions (b.c). We have obtained exact results for the free energy and theCasimir force for antiperiodic, Neumann, Dirichlet, and Neumann-Dirichlet mixedb.c. in 1<d<4 dimensions. For the Casimir force, finite-size scaling is foundto be valid for all b.c.. For the free energy, finite-size scaling is valid in1<d<3 and 3<d<4 dimensions for antiperiodic, Neumann, and Dirichlet b.c., butlogarithmic deviations from finite-size scaling exist in d=3 dimensions forNeumann and Dirichlet b.c.. This is explained in terms of the borderlinedimension d*=3, where the critical exponent of the Gaussian surface energydensity vanishes. For Neumann-Dirichlet b.c., finite-size scaling is stronglyviolated above T_c for 1<d<4. Our results include an exact description of thedimensional crossover between the d-dimensional finite-size critical behaviornear bulk T_c and the (d-1)-dimensional critical behavior near T_c,film(L).This dimensional crossover is illustrated for the critical behavior of thespecific heat. For 2<d<4, the Gaussian results are reformulated as one-loopcontributions of the phi^4 theory at fixed dimension and are compared with theepsilon=4-d expansion results as well as with d=3 Monte Carlo data. For d=2,the Gaussian results for the Casimir force scaling function are compared withthose for the Ising model; unexpected exact relations are found between theGaussian and Ising scaling functions. For both the Gaussian and the Ising modelit is shown that anisotropic couplings imply nonuniversal scaling functions ofthe Casimir force. Our Gaussian results provide the basis for the investigationof finite-size effects of the mean spherical model with nonperiodic b.c..

Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension