Thermodynamic Casimir effect: Universality and Corrections to Scaling

Abstract

We study the thermodynamic Casimir force for films in the three-dimensional Ising universality class with symmetry breaking boundary conditions. We focus on the effect of corrections to scaling and probe numerically the universality of our results. In particular we check our hypothesis that corrections are well described by an effective thickness L_{0,eff}=L_0+c (L_0+L_s)^{1-ω} +L_s, where c and L_s are system specific parameters and ω\approx 0.8 is the exponent of the leading bulk correction. We simulate the improved Blume-Capel model and the Ising model on the simple cubic lattice. First we analyse the behaviour of various quantities at the critical point. Taking into account corrections \propto L_0^{-ω} in the case of the Ising model, we find good consistency of results obtained from these two different models. In particular we get from the analysis of our data for the Ising model for the difference of Casimir amplitudes Δ_{+-}-Δ_{++}=3.200(5), which nicely compares with Δ_{+-}-Δ_{++}=3.208(5) obtained by studying the improved Blume-Capel model. Next we study the behaviour of the thermodynamic Casimir force for large values of the scaling variable x=t [L_0/ξ_0]. This behaviour can be obtained up to an overall amplitude by expressing the partition function of the film in terms of eigenvalues and eigenstates of the transfermatrix and boundary states. Here we show how this overall amplitude can be computed with high accuracy. Finally we discuss our results for the scaling functions θ_{+-} and θ_{++} of the thermodynamic Casimir force for the whole range of the scaling variable. We conclude that our numerical results are in accordance with universality. Corrections to scaling are well approximated by an effective thickness.

35 pages, 5 figures, various typos corrected

References in corpus (11)

• The critical exponents of the superfluid transition in He4
• The Casimir effect: from quantum to critical fluctuations
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling
• Monte Carlo simulation results for critical Casimir forces
• The thermodynamic Casimir force: A Monte Carlo study of the crossover between the ordinary and the normal surface universality class
• Thermodynamic Casimir effect for films in the 3D Ising universality class: Symmetry breaking boundary conditions
• Aspect-ratio dependence of thermodynamic Casimir forces
• Critical Casimir forces for Ising films with variable boundary fields
• Interplay of critical Casimir and dispersion forces
• The free energy in a magnetic field and the universal scaling equation of state for the three-dimensional Ising model

Cited by in corpus (45)

• Finite-size scaling at quantum transitions
• Coherent and dissipative dynamics at quantum phase transitions
• Collective behavior of colloids due to critical Casimir interactions
• Nonadditivity of Critical Casimir Forces
• Boundary critical behavior of the three-dimensional Heisenberg universality class
• 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
• Restoring isotropy in a three-dimensional lattice model: The Ising universality class
• Critical behavior in the presence of an order-parameter pinning field
• Critical Casimir forces between homogeneous and chemically striped surfaces
• Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques
• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• Casimir force in the O(n -> infinity) model with free boundary conditions
• Conformal symmetry of the critical 3D Ising model inside a sphere
• Universal behavior of two-dimensional bosonic gases at Berezinskii-Kosterlitz-Thouless transitions
• Critical Casimir force in the presence of random local adsorption preference
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Direct calculation of the critical Casimir force in a binary fluid
• Two- and three-point functions at criticality: Monte Carlo simulations of the improved three-dimensional Blume-Capel model
• OPE Coefficients of the 3D Ising model with a trapping potential
• Critical Casimir forces in the presence of random surface fields
• Conformal perturbation of off-critical correlators in the 3D Ising universality class
• Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface
• Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking
• 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
• Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries
• Critical Casimir forces in a magnetic system: An experimental protocol
• Simulating the All-Order Strong Coupling Expansion V: Ising Gauge Theory
• A variance reduced estimator of the connected two-point function in the presence of a broken Z_2 symmetry
• Ising string beyond Nambu-Goto
• Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class
• The ordinary surface universality class of the three-dimensional O($N$) model
• The Ising universality class in dimension three: corrections to scaling
• Critical energy density of O$(n)$ models in $d=3$
• Numerical estimation of structure constants in the 3d Ising CFT through Markov chain UV sampler
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality
• Spin models in three dimensions: Adaptive lattice spacing
• Effective binding potential from Casimir interactions: the case of the Bose gas
• Surface critical behavior of the three-dimensional O(3) model
• Energy trapped Ising model
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Robust orbital diamagnetism of correlated Dirac fermions in chiral Ising universality class