Regensburg 2007 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 15: Internal Symposium: Finite size effects at phase transitions
DY 15.2: Hauptvortrag
Dienstag, 27. März 2007, 14:30–15:00, H2
Successes and limitations of current renormalization group approaches to the study of finite size effects — •Hans Werner Diehl and Daniel Grüneberg — Fachbereich Physik, Universität Duisburg-Essen, Campus Duisburg, D-47048 Duisburg, Germany
A survey of what current renormalization group (RG) approaches based on expansions about the upper critical dimension can contribute to the study of finite size effects near continuous bulk phase transitions is given. In particular, systems in slab geometries — the simplest geometries encountered in studies of the Casimir effect — are considered. Recent work1,2 revealing that previous approaches break down at the bulk critical temperature Tc in those cases where the boundary conditions entail the presence of a zero mode at the level of Landau theory is elucidated. The proposed reorganization of RG-improved perturbation theory makes the theory well-defined at Tc and yields temperature dependent scaling functions in conformity with phenomenological analyticity requirements. This improves the theory for slabs under such “zero-mode boundary conditions” basically to the level known from the cases of boundary conditions for which no zero modes are present at Tc in Landau theory. The challenge to go beyond this level by developing successful feasible approximation schemes by which the finite size behavior can be systematically studied for slabs also for temperatures below Tc, including eventual dimensional crossovers, remains.
1 H. W. Diehl, D. Grüneberg, and M. A. Shpot, Europhys. Lett. 75, 241 (2006), cond-mat/0605293.
2 D. Grüneberg, H. W. Diehl, and D. M. Dantchev, to be published.