  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.
