Dresden 2006 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 42: Critical Phenomena and Phase Transitions II

DY 42.2: Vortrag

Donnerstag, 30. März 2006, 11:15–11:30, H\"UL 186

Casimir effect in the presence of van-der-Waals-type interactions: exact results for the spherical model with periodic boundary conditions — •Daniel Grüneberg¹, Daniel Dantchev^1,2, and H. W. Diehl¹ — ¹Fachbereich Physik, Universität Duisburg-Essen, D-45117 Essen, Germany — ²Institute of Mechanics—BAS, Acad. G. Bonchev St. bl. 4, 1113 Sofia, Bulgaria

It is studied how the Casimir effect in d-dimensional slabs with 2<d<4 and periodic boundary conditions is affected at and near the bulk critical temperature T_c,∞ by long-range pair interactions whose potential decays as b x^−(d+σ) as x→∞, with 2<σ<4 and 2<d+σ≤ 6. While such interactions decay sufficiently fast to leave bulk critical exponents and other universal bulk quantities unchanged, they entail important modifications of the standard scaling behavior of the excess free energy and the Casimir force, and give algebraically decaying contributions that dominate the behavior of these quantities for T≠ T_c,∞ as a function of the slab’s thickness. An appropriate mean spherical model in a slab geometry with periodic boundary conditions is solved exactly. The scaling functions of the excess free energy and the Casimir force are determined, including the contributions to first order in the usual leading irrelevant scaling field g_ω and the scaling field g_σ to which the long-range interactions give rise. In the case d+σ=6, which includes that of nonretarded van-der-Waals interactions in d=3 dimensions, the power laws of the corrections to scaling ∝ b of the spherical model get modified by logarithms. The origin of these anomalies is clarified.