Critical Casimir force in slab geometry with finite aspect ratio: Analytic calculation above and below Tc
Critical Casimir force in slab geometry with finite aspect ratio: Analytic calculation above and below Tc
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具有有限长宽比的板坯几何形状中的临界卡西米尔力：高于和低于 Tc 的解析计算
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发表时间：
2009
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通讯作者：
V. Dohm
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作者：
V. Dohm
基于O（n）对称各向同性φ4短程相互作用场理论，研究了d维L <$d-1×L平板几何中的临界Casimir力，其中有限长宽比ρ=L/L <$.在大n极限下得到了精确的结果。当n=1时，给出了在固定维数d=3时微扰方法的结果，它描述了在ρ = 1/4范围内对纵横比的依赖性。我们对Casimir力标度函数的解析结果（ρ=1/4）与最近的MonteCarlo数据吻合得很好，这些数据是针对具有高于、等于和低于Tc的周期性边界条件的三维板状Ising模型的。
We study the critical Casimir force in a d-dimensional L∥d-1×L slab geometry with a finite aspect ratio ρ=L/L∥ above, at, and below Tc on the basis of the O(n) symmetric isotropic φ4 field theory with short-range interactions. Exact results are obtained in the large-n limit. For n=1, the result of a perturbation approach at fixed dimension d=3 is presented that describes the dependence on the aspect ratio in the range ρ≳1/4. Our analytic result for the Casimir force scaling function for ρ=1/4 agrees well with recent Monte Carlo data for the three-dimensional Ising model in slab geometry with periodic boundary conditions above, at, and below Tc.