Critical Casimir forces for ${\cal O}(n)$ systems with long-range interaction in the spherical limit

Details Critical Casimir forces for ${\cal O}(n)$ systems with long-range interaction in the spherical limit Critical Casimir forces for ${\cal O}(n)$ systems with long-range interaction in the spherical limit

2004-06-21

arxiv.org/abs/cond-mat/0406480v1

Physics

Condensed Matter

Statistical Mechanics

13 pages, revtex, 8 figures

Scientific paper

10.1103/PhysRevE.70.066106

We present exact results on the behavior of the thermodynamic Casimir force and the excess free energy in the framework of the $d$-dimensional spherical model with a power law long-range interaction decaying at large distances $r$ as $r^{-d-\sigma}$, where $\sigmaT_c$ and $TT_c$ it decays as $L^{-d-\sigma}$, where $L$ is the thickness of the film. We consider both the case of a finite system that has no phase transition of its own, when $d-1<\sigma$, as well as the case with $d-1>\sigma$, when one observes a dimensional crossover from $d$ to a $d-1$ dimensional critical behavior. The behavior of the force along the phase coexistence line for a magnetic field H=0 and $T1$ and a decreasing one for $\sigma<1$. For any $d$ and $\sigma$ the minimum of the force at $T=T_c$ is always achieved at some $H\ne 0$.

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