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 th
at, 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 $f_{mathrm C}(wto 0)-f_{mathrm C}(w=0)sim w^2$. 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.
We present a system exhibiting giant proximity effects which parallel observations in superfluid helium (Perron et al, Nature Physics V. 6, 499 (2010)) and give a theoretical explanation of these phenomena based on the mesoscopic picture of phase coe
xistence in finite systems. Our theory is confirmed by MC simulation studies. Our work demonstrates that such action-at-a-distance can occur in classical systems involving simple or complex fluids, such as colloid-polymer mixtures, or ferromagnets.
Monte Carlo simulations based on an integration scheme for free energy differences is used to compute critical Casimir forces for three-dimensional Ising films with various boundary fields. We study the scaling behavior of the critical Casimir force,
including the scaling variable related to the boundary fields. Finite size corrections to scaling are taken into account. We pay special attention to that range of surface field strengths within which the force changes from repulsive to attractive upon increasing the temperature. Our data are compared with other results available in the literature.
If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter
fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.
Effective Casimir forces induced by thermal fluctuations in the vicinity of bulk critical points are studied by means of Monte Carlo simulations in three-dimensional systems for film geometries and within the experimentally relevant Ising and XY univ
ersality classes. Several surface universality classes of the confining surfaces are considered, some of which are relevant for recent experiments. A novel approach introduced previously EPL 80, 60009 (2007), based inter alia on an integration scheme of free energy differences, is utilized to compute the universal scaling functions of the critical Casimir forces in the critical range of temperatures above and below the bulk critical temperature. The resulting predictions are compared with corresponding experimental data for wetting films of fluids and with available theoretical results.
The excess adsorption $Gamma $ in two-dimensional Ising strips $(infty times L)$ subject to identical boundary fields, at both one-dimensional surfaces decaying in the orthogonal direction $j$ as $-h_1j^{-p}$, is studied for various values of $p$ and
along various thermodynamic paths below the critical point by means of the density-matrix renormalization-group method. The crossover behavior between the complete wetting and critical adsorption regimes, occurring in semi-infinite systems, are strongly influenced by confinement effects. Along isotherms $T=const$ the asymptotic power law dependences on the external bulk field, which characterize these two regimes, are undercut by capillary condensation. Along the pseudo first-order phase coexistence line of the strips, which varies with temperature, we find a broad crossover regime where both the thickness of the wetting film and $Gamma$ increase as function of the reduced temperature $tau$ but do not follow any power law. Above the wetting temperature the order parameter profiles are not slab-like but exhibit wide interfacial variations and pronounced tails. Inter alia, our explicit calculations demonstrate that, contrary to opposite claims by Kroll and Lipowsky [Phys. Rev. B {bf 28}, 5273 (1983)], for $p=2$ critical wetting transitions do exist and we determine the corresponding wetting phase diagram in the $(h_1,T)$ plane.
The confinement of critical fluctuations in soft media induces critical Casimir forces acting on the confining surfaces. The temperature and geometry dependences of such forces are characterized by universal scaling functions. A novel approach is pre
sented to determine them for films via Monte Carlo simulations of lattice models. The method is based on an integration scheme of free energy differences. Our results for the Ising and the XY universality class compare favourably with corresponding experimental results for wetting layers of classical binary liquid mixtures and of 4He, respectively.
Recent experimental data for the complete wetting behavior of pure 4He and of 3He-4He mixtures exposed to solid substrates show that there is a change of the corresponding film thicknesses L upon approaching thermodynamically the lambda-transition an
d the tricritical end point, respectively, which can be attributed to critical Casimir forces f_C. We calculate the scaling functions vartheta of f_C within models representing the corresponding universality classes. For the mixtures our analysis provides an understanding of the rich behavior of vartheta deduced from the experimental data and predicts the crossover behavior between the tricritical point and the lambda-transition of pure 4He which are connected by a line of critical points. The formation of a soft-mode phase within the wetting films gives rise to a pronounced maximum of f_C below the tricritical point as observed experimentally. Near the tricritical point we find logarithmic corrections ~L^(-3)(ln L)^(1/2) for the leading behavior of vartheta dominating the contributions from the background dispersion forces.
