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

Abstract

We study the crossover from the ordinary to the normal surface universality class in the three-dimensional Ising 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_{h_1}=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 h_1. Finally we study the approach to the strong adsorption limit h_1 \rightarrow \infty. 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 3D Ising model, [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.

34 pages, 10 figures, discussion extended, typos corrected, references added

References in corpus (9)

• The Casimir effect: from quantum to critical fluctuations
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Monte Carlo simulation results for critical Casimir forces
• Tunability of Critical Casimir Interactions by Boundary Conditions
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions
• Critical Casimir effect for colloids close to chemically patterned substrates
• Critical Casimir forces steered by patterned substrates
• Short-time critical dynamics at perfect and non-perfect surface

Cited by in corpus (18)

• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Critical Casimir Effect: Exact Results
• Critical behavior in the presence of an order-parameter pinning field
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Critical Casimir forces in the presence of random surface fields
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
• The ordinary surface universality class of the three-dimensional O($N$) model
• Effective interaction between a colloid and a soft interface near criticality
• Finite-size corrections to the energy spectra of gapless one-dimensional systems in the presence of boundaries
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Surface critical behavior of the three-dimensional O(3) model
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• Critical Three-Dimensional Ising Model on Spheriods from the Conformal Bootstrap