Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 18: Critical Phenomena and Phase Transitions

DY 18.3: Vortrag

Montag, 12. März 2018, 16:00–16:15, BH-N 333

Disassembling Casimir scaling functions at finite aspect ratios — •Hendrik Hobrecht and Fred Hucht — Fakultät für Physik, Universität Duisburg-Essen, 47048 Duisburg

The finite-size scaling functions for the free energy of the two-dimensional Ising universality class are known exactly only either for finite aspect ratios at criticality due to conformal field theory (CFT), or for thin films at arbitrary temperatures. Beyond the thin films and CFT there are but a few results, namely for the torus, the open cylinder, and approaches for topologically more exotic forms like the open Möbius strip and the Klein bottle. Despite their role as potential for the critical Casimir force, even less is known in the presence of surface fields. We present a systematic calculation of the interlink between those limiting cases, implementing both symmetric (++) and asymmetric (+-) symmetry-breaking boundary conditions (BCs) on the cylinder with finite aspect ratio, as well as the often discussed Brascamp-Kunz BC. We show that the scaling limit of the latter one is indeed equal to open boundaries, as both are believed to represent Dirichlet BCs. An impressive feature of these scaling functions is the possibility to disassemble them not only into recurring bulk, surface, and finite-size contributions, but even beyond. We can distinguish different building blocks for the surfaces and surface fields, as well as for the breaking of the Z₂-symmetry and the surface tension due to imposed domain walls.