Critical Casimir forces in the presence of random surface fields

Abstract

We study critical Casimir forces (CCF) $f_{\mathrm{C}}$ for films of thickness $L$ which in the three-dimensional bulk belong to the Ising universality class and which are exposed to random surface fields (RSF) on both surfaces. We consider the case that, in the absence of RSF, the surfaces of the film belong to the surface universality class of the so-called ordinary transition. We carry out a finite-size scaling analysis and show that for weak disorder CCF still exhibit scaling, acquiring a random field scaling variable $w$ which is zero for pure systems. We confirm these analytic predictions by MC simulations. Moreover, our MC data show that $f_{\mathrm{C}}$ varies as $f_{\mathrm{C}}(w\to 0)-f_{\mathrm{C}}(w=0)\sim w^2$. Asymptotically, for large $L$, $w$ scales as $w\sim L^{-0.26}\to 0$ indicating that this type of disorder is an irrelevant perturbation of the ordinary surface universality class. However, for thin films such that $w\simeq 1$, we find that the presence of RSF with vanishing mean value increases significantly the strength of CCF, as compared to systems without them, and shifts the extremum of the scaling function of $f_{\mathrm{C}}$ towards lower temperatures. But $f_{\mathrm{C}}$ remains attractive.

20 pages, 3 figures

References in corpus (35)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• 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 Magnetization of the 3D Ising Model
• Casimir forces in binary liquid mixtures
• 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 Effect in ${}^4$He Films near $T_{\lambda }$: Monte Carlo Results
• Tunability of Critical Casimir Interactions by Boundary Conditions
• Critical phenomena at perfect and non-perfect surfaces
• 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
• Crossover from Attractive to Repulsive Casimir Forces and Vice Versa
• Casimir interactions in Ising strips with boundary fields: exact results
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Fluctuation-Induced Interaction between Randomly Charged Dielectrics
• Crossover of Critical Casimir forces between different surface universality classes
• Salt-induced changes of colloidal interactions in critical mixtures
• Near-Surface Long-Range Order at the Ordinary Transition
• Aspect-ratio dependence of thermodynamic Casimir forces
• Critical Casimir forces for Ising films with variable boundary fields
• Interaction between Heterogeneously Charged Surfaces: Surface Patches and Charge Modulation
• Off-critical Casimir effect in Ising Slabs with Symmetric Boundary Conditions in d=3
• Trapping colloids near chemical stripes via critical Casimir forces
• Correlation Function in Ising Models
• Effects of weak surface fields on the density profiles and adsorption of a confined fluid near bulk criticality
• A Monte Carlo study of surface critical phenomena: The special point
• Solvation force for long ranged wall-fluid potentials
• Critical Casimir Effect in 3He-4He films
• Critical Adsorption in Systems with Weak Surface Field: The Renormalization-Group Approach
• Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model
• Critical Casimir force in the presence of random local adsorption preference

Cited by in corpus (9)

• Critical Casimir Effect: Exact Results
• 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 Casimir Force between Inhomogeneous Boundaries
• Effective Pair Interaction of Patchy Particles in Critical Fluids
• Repulsive to Attractive Fluctuation-Induced Forces in Disordered Landau-Ginzburg Model
• Fluctuation induced forces in critical films with disorder at their surfaces
• Manipulation and amplification of the Casimir force through surface fields using helicity
• Surface alignment disorder and pseudo-Casimir forces in smectic-A liquid crystalline films