Casimir force in the O(n→∞) model with free boundary conditions.
We present results for the temperature behavior of the Casimir force for a system with a film geometry with thickness L subject to free boundary conditions and described by the n→∞ limit of the O(n) model. These results extend over all temperatures, including the critical regime near the bulk critical temperature Tc, where the critical fluctuations determine the behavior of the force, and temperatures well below it, where its behavior is dictated by the Goldstone mode contributions. The temperature behavior when the absolute temperature, T, is a finite distance below Tc, up to a logarithmic-in-L proximity of the bulk critical temperature, is obtained both analytically and numerically; the critical behavior follows from numerics. The results resemble-but do not duplicate-the experimental curve behavior for the force obtained for He4 films.
Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095-1547, USA and Institute of Mechanics-BAS, Academic Georgy Bonchev St. building 4, 1113 Sofia, Bulgaria.
Daniel
D
Dantchev
Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095-1547, USA.
Jonathan
J
Bergknoff
Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, California 90095-1547, USA.
Joseph
J
Rudnick