Jonathan Bergknoff, Daniel Dantchev, Joseph Rudnick
We study the Casimir force in a film with free boundary conditions described by the $n\to\infty$ limit of the O(n) models. Via exact calculations we reduce the model to an one dimensional model the properties of which we determine numerically, near the critical region, and in an exact analytical manner in the low-temperature regime. The results resemble the experimental curve behavior for the force obtained for $^4$He films.
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http://arxiv.org/abs/1210.1452
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