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.
We study the survival of a prey that is hunted by N predators. The predators perform independent random walks on a square lattice with V sites and start a direct chase whenever the prey appears within their sighting range. The prey is caught when a p
redator jumps to the site occupied by the prey. We analyze the efficacy of a lazy, minimal-effort evasion strategy according to which the prey tries to avoid encounters with the predators by making a hop only when any of the predators appears within its sighting range; otherwise the prey stays still. We show that if the sighting range of such a lazy prey is equal to 1 lattice spacing, at least 3 predators are needed in order to catch the prey on a square lattice. In this situation, we establish a simple asymptotic relation ln(Pev)(t) sim (N/V)2ln(Pimm(t)) between the survival probabilities of an evasive and an immobile prey. Hence, when the density of the predators is low N/V<<1, the lazy evasion strategy leads to the spectacular increase of the survival probability. We also argue that a short-sighting prey (its sighting range is smaller than the sighting range of the predators) undergoes an effective superdiffusive motion, as a result of its encounters with the predators, whereas a far-sighting prey performs a diffusive-type motion.
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 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.
