Boundary conditions and the critical Casimir force on an Ising model film: exact results in one and two dimensions

Details Boundary conditions and the critical Casimir force on an Ising model film: exact results in one and two dimensions Boundary conditions and the critical Casimir force on an Ising model film: exact results in one and two dimensions

2010-01-06

arxiv.org/abs/1001.0994v1

Physics

Condensed Matter

Statistical Mechanics

18 page, 10 figures

Scientific paper

Finite size effect in critical systems can be interpreted as universal Casimir forces. Here we compare the Casimir force for free, periodic and antiperiodic boundary conditions in the exactly calculable case of the Ising model in one and two dimensions. We employ a new procedure which allows us to calculate the Casimir force with periodic and antiperiodic boundary conditions analytically in a transparent manner. Quite interestingly, we find an attractive Casimir force for the case of periodic boundary condition but a repulsive Casimir force for the anti-periodic one.

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