Critical Casimir effect: Exact results

In any medium there are fluctuations due to temperature or the quantum nature of its constituents. If a material body is immersed into such medium, shape and properties constituents modify surrounding fluctuations. in same second then — addition all direct interactions between them modifications first influence body. This mutual results force these bodies. excitations which mediate effective interaction bodies, massless, this long-ranged nowadays known as Casimir force. fluctuating consists confined electromagnetic field vacuum, one speaks mechanical effect. case that order parameter fields fluctuates – differences number densities concentrations corresponding long-ranged, critical holds, e.g., systems undergo second-order phase transition thermodynamically located near point, for with broken continuous symmetry exhibiting Goldstone mode excitations. Here we review currently available exact concerning effect encompassing one-dimensional Ising, XY, Heisenberg models, two-dimensional Ising model, Gaussian spherical well mean XY model. Special attention paid boundary conditions on behavior We present both classical if system possesses point at non-zero temperature, undergoing zero function certain parameters. As confinements consider film, sphere–plane, sphere–sphere geometries. discuss governed by short-ranged, subleading (i.e., van der Waals type), leading interactions. put proper context make self-contained possible, basic facts about theory transitions, phenomena systems, finite-size scaling recalled. Whenever discussion relevance towards an understanding experiments presented. The eventual applicability devices pointed out, too.