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.

arXiv comment34 pages, 10 figures, discussion extended, typos corrected, references added

References in corpus (25)

• Critical Phenomena and Renormalization-Group Theory
• A Finite Size Scaling Study of Lattice Models in the three-dimensional Ising Universality Class
• The Theory of Boundary Critical Phenomena
• Critical Casimir effect in classical binary liquid mixtures
• The Casimir effect: from quantum to critical fluctuations
• Casimir forces in binary liquid mixtures
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Monte Carlo simulation results for critical Casimir forces
• Massive Field-Theory Approach to Surface Critical Behavior in Three-Dimensional Systems
• The Thermodynamic Casimir Effect in ${}^4$He Films near $T_{\lambda }$: Monte Carlo Results
• Tunability of Critical Casimir Interactions by Boundary Conditions
• Ordinary, extraordinary, and normal surface transitions: extraordinary-normal equivalence and simple explanation of $|T-T_c{|}^{2-\alpha }$ singularities
• Surface and bulk transitions in three-dimensional O(n) models
• The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results
• Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Casimir interactions in Ising strips with boundary fields: exact results
• Critical Casimir effect for colloids close to chemically patterned substrates
• Crossover of Critical Casimir forces between different surface universality classes
• Critical phenomena at perfect and non-perfect surfaces
• Normal and lateral critical Casimir forces between colloids and patterned substrates
• Universal amplitude ratios in the 3D Ising Universality Class
• Critical Casimir forces steered by patterned substrates
• Yet another method to compute the thermodynamic Casimir force in lattice models
• Short-time critical dynamics at perfect and non-perfect surface

Cited by in corpus (44)

• Boundary and Interface CFTs from the Conformal Bootstrap
• Defects in conformal field theory
• Collective behavior of colloids due to critical Casimir interactions
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• Truncatable bootstrap equations in algebraic form and critical surface exponents
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• 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 forces for Ising films with variable boundary fields
• Critical Casimir Effect: Exact Results
• The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model
• Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions
• Critical behavior in the presence of an order-parameter pinning field
• A Monte Carlo study of surface critical phenomena: The special point
• Critical adsorption and critical Casimir forces in the canonical ensemble
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Critical Casimir Forces for Films with Bulk Ordering Fields
• Structure and aggregation of colloids immersed in critical solvents
• Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions
• Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
• Casimir force in the O(n -> infinity) model with free boundary conditions
• Conformal symmetry of the critical 3D Ising model inside a sphere
• Critical Casimir force in the presence of random local adsorption preference
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Critical Casimir forces from the equation of state of quantum critical systems
• Critical Casimir forces in the presence of random surface fields
• Casimir force in the rotor model with twisted boundary conditions
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• 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
• Why boundary conditions do not generally determine the universality class for boundary critical behavior
• Critical Casimir forces in a magnetic system: An experimental protocol
• 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
• Fluctuation induced forces in critical films with disorder at their surfaces
• Manipulation and amplification of the Casimir force through surface fields using helicity
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Finite-size scaling of the magnetization probability density for the critical Ising model in slab geometry
• 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