Critical Casimir Interactions Between Spherical Particles in the Presence of the Bulk Ordering Fields

The spatial suppression of order parameter fluctuations in a critical media produces Critical Casimir forces acting on confining surfaces. This scenario is realized in a critical binary mixture near the demixing transition point that corresponds to the second order phase transition of the Ising universality class. Due to these critical interactions similar colloids, immersed in a critical binary mixture near the consolute point, exhibit attraction. The numerical method for computation of the interaction potential between two spherical particles using Monte Carlo simulations for the Ising model is proposed. This method is based on the integration of the local magnetization over the applied local magnetic field. For the stronger interaction the concentration of the component of the mixture that does not wet colloidal particles, should be larger, than the critical concentration. The strongest amplitude of the interactions is observed below the critical point.Comment: 7 pages, 4 figure

Critical Casimir Interactions and Percolation: the quantitative description of critical fluctuations

Casimir forces in a critical media are produced by spatial suppression of order parameter fluctuations. In this paper we address the question how fluctuations of a critical media relates the magnitude of critical Casimir interactions. Namely, for the Ising model we express the potential of critical Casimir interactions in terms of Fortuin-Kasteleyn site-bond correlated percolation clusters. These clusters are quantitative representation of fluctuations in the media. New Monte Carlo method for the computation of the Casimir force potential which is based on this relation is proposed. We verify this method by computation of Casimir interactions between two disks for 2D Ising model. The new method is also applied to the investigation of non-additivity of the critical Casimir potential. The non-additive contribution to three-particles interaction is computed as a function of the temperature.Comment: 13 pages, 4 figure

Two-temperature Langevin dynamics in a parabolic potential

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the X and the Y directions. In the stationary regime the system is described by a non-trivial particle position distribution P(x,y), which we determine explicitly. We show that this distribution corresponds to a non-equilibrium stationary state, characterised by the presence of space-dependent particle currents which exhibit a non-zero rotor. Theoretical results are confirmed by the numerical simulations.Comment: 9 pages, 2 figure

Monte-Carlo study of anisotropic scaling generated by disorder

We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $\xi_\parallel$ in the direction along defects, and a perpendicular correlation length $\xi_\perp$ in the direction perpendicular to the lines. Both $\xi_\parallel$ and $\xi_\perp$ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents $\nu_\parallel$ and $\nu_\perp$ take different values. This property is specific for anisotropic scaling and the ratio $\nu_\parallel/\nu_\perp$ defines the anisotropy exponent $\theta$. Estimates of quantitative characteristics of the critical behaviour for such systems were only obtained up to now within the renormalization group approach. We report a study of the anisotropic scaling in this system via Monte Carlo simulation of the three-dimensional system with Ising spins and non-magnetic impurities arranged into randomly distributed parallel lines. Several independent estimates for the anisotropy exponent $\theta$ of the system are obtained, as well as an estimate of the susceptibility exponent $\gamma$. Our results corroborate the renormalization group predictions obtained earlier.Comment: 22 pages, 9 figure