Many-body critical Casimir interactions in colloidal suspensions

TL;DR

This paper investigates fluctuation-induced Casimir forces in colloidal suspensions near criticality, introducing an efficient simulation method and revealing complex many-body effects that challenge traditional decomposition approaches.

Contribution

The authors develop a highly efficient cluster Monte Carlo algorithm for simulating many-body critical Casimir interactions in colloids, demonstrating the importance of symmetry and many-body effects.

Findings

Monte Carlo results match exact two-dimensional predictions.

Finite system behavior depends on Z2 symmetry breaking.

Many-body interactions cannot be accurately decomposed into pairwise terms.

Abstract

We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point in two dimensions perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the $Z_{2}$ symmetry of the system is broken by the particles. Eventually we present Monte Carlo results for the three-body Casimir interaction potential and take a close look onto the case of one particle in the vicinity of two adjacent particles, which can be calculated from the two-particle interaction by a conformal mapping. These results emphasize the failure of the common decomposition approach for many-particle critical Casimir interactions.