Thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class

We study the crossover from the ordinary to the normal surface universality class in the three-dimensional Ising bulk universality class. This crossover is relevant for the behavior of films of binary mixtures near the demixing point and a weak adsorption at one or both surfaces. We perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. We consider systems with film geometry, where various boundary conditions are applied. We discuss corrections to scaling that are caused by the surfaces and their relation with the so called extrapolation length. To this end, we analyze the behavior of the magnetization profile near the surfaces of films. We obtain an accurate estimate of the renormalization-group exponent y(h1) = 0.7249(6) for the ordinary surface universality class. Next we study the thermodynamic Casimir force in the crossover region from the ordinary to the normal surface universality class. To this end, we compute the Taylor expansion of the crossover finite-size scaling function up to the second order in h(1) around h(1) = 0, where h(1) is the external field at one of the surfaces. We check the range of applicability of the Taylor expansion by simulating at finite values of h1. Finally, we study the approach to the strong adsorption limit h(1) -> infinity. Our results confirm the qualitative picture that emerges from exact calculations for stripes of the two-dimensional Ising model [D. B. Abraham and A. Maciolek, Phys. Rev. Lett. 105, 055701 (2010)], mean-field calculations, and preliminary Monte Carlo simulations of the Ising model on the simple cubic lattice [T. F. Mohry et al., Phys. Rev. E 81, 061117 (2010)]: For certain choices of h(1) and the thickness of the film, the thermodynamic Casimir force changes sign as a function of the temperature, and for certain choices of the temperature and h(1), it also changes sign as a function of the thickness of the film.