Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model

Abstract

We study the thermodynamic Casimir force between a spherical object and a plate. We consider the bulk universality class of the three-dimensional Ising model, which is relevant for experiments on binary mixtures. To this end, we simulate the improved Blume-Capel model. Following Hucht, we compute the force by integrating energy differences over the inverse temperature. We demonstrate that these energy differences can be computed efficiently by using a particular cluster algorithm. Our numerical results for strongly symmetry breaking boundary conditions are compared with the Derjaguin approximation for small distances and the small sphere expansion for large distances between the sphere and the plate.

32 pages, 16 figures, reference added, value of the parameter i_m in section V A corrected

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• Critical Casimir Interactions Between Spherical Particles in the Presence of the Bulk Ordering Fields
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• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
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• Anisotropic scaling of the two-dimensional Ising model I: the torus
• Critical Casimir force scaling functions of the two-dimensional Ising model at finite aspect ratios
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking
• Critical Casimir forces between defects in the 2D Ising model
• 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
• Effective Pair Interaction of Patchy Particles in Critical Fluids
• Critical Casimir forces in a magnetic system: An experimental protocol
• Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces
• A variance reduced estimator of the connected two-point function in the presence of a broken Z_2 symmetry
• Effective interaction between a colloid and a soft interface near criticality
• Conformal field theory of critical Casimir forces between surfaces with alternating boundary conditions in two dimensions
• Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class
• Critical Casimir effects in 2D Ising model with curved defect lines
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Spin models in three dimensions: Adaptive lattice spacing
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations
• The interface tension in the improved Blume-Capel model