Fluctuation-induced interactions in nematics with disordered anchoring energy

Manipulation and amplification of the Casimir force through surface fields using helicity

We present both exact and numerical results for the behavior of the Casimir force in O(n) systems with a finite extension L in one direction when the system is subjected to surface fields that induce helicity in the order parameter. We show that for such systems, the Casimir force in certain temperature ranges is of the order of L^{-2}, both above and below the critical temperature, T_{c}, of the bulk system. An example of such a system would be one with chemically modulated bounding surfaces, in which the modulation couples directly to the system's order parameter. We demonstrate that, depending on the parameters of the system, the Casimir force can be either attractive or repulsive. The exact calculations presented are for the one-dimensional XY and Heisenberg models under twisted boundary conditions resulting from finite surface fields that differ in direction by a specified angle, and the three-dimensional Gaussian model with surface fields in the form of plane waves that are shifted in phase with respect to each other. Additionally, we present exact and numerical results for the mean-field version of the three-dimensional O(2) model with finite surface fields on the bounding surfaces. We find that all significant results are consistent with the expectations of finite-size scaling.

Critical Casimir force in the presence of random local adsorption preference

We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p, the system exhibits a crossover between an attractive and a repulsive force. At p=1/2, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.