Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Montag
DY 16 Phase Transitions
Zeit: Montag 16:45–18:00 Raum: H2
DY 16.1 Mo 16:45 H2
Vortex Loop Percolation in XY and Ginzburg-Landau Model —
•Axel Krinner, Elmar Bittner, and Wolfhard Janke — Institut
für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11,
04109 Leipzig, Germany
We study the geometrically defined vortex network in the vicinity of
the critical point in the XY and Ginzburg-Landau model. Using highprecision
Monte Carlo techniques we consider the alternative formulation
of the geometrical excitations in relation to the global O(2)-symmetry
breaking, and check if both of them exhibit the same critical behaviour
leading to a consistent description of the phase transition. Different percolation
observables are taken into account and compared with each other.
DY 16.2 Mo 17:00 H2
Equilibrium Crystal Shapes in Three Dimensions — •Andreas
Nußbaumer, Elmar Bittner, and Wolfhard Janke — Institut
für Theoretische Physik, Universität Leipzig, Augustusplatz 10/11, 04109
Leipzig, Germany
The multimagnetic algorithm simulates an artifical ensemble where every
value of the magnetisation has the same probability. Still, simulations
of simple models show barriers in the magnetisation that scale with the
inverse temperature β and the system size L. Making use of analytic
work by Leung and Zia [1], Neuhaus and Hager [2] recently explained
this behaviour in the case of the two-dimensional Ising model with the
occurrence of a geometrically induced first-order transition from a droplet
to a strip domain.
Using Fourier coefficients to define the geometric anisotropy of a configuration
a comparison with an analytical description of the transition
behaviour (deformation of a droplet into a stripe) was possible. From the
scaling of the anisotropy for different system sizes when simulated with
Kawasaki dynamics (M = const.) a value for the barrier size was obtained.
For the three-dimensional case a set of new transitions could be
identified and the crystal shapes during the transitions were measured.
[1] K. Leung and R. Zia, Geometrically induced transitions between equilibrium
crystal shapes, J. Phys. A 23, 4593 (1990).
[2] T. Neuhaus and J. Hager, 2D crystal shapes, droplet condensation,
and exponential slowing down in simulations of first-order phase transitions,
Stat. Phys. 113, 47 (2003).
DY 16.3 Mo 17:15 H2
The Harris-Luck Criterion for Random Lattices — •Wolfhard
Janke and Martin Weigel — Institut für Theoretische Physik, Universität
Leipzig, Augustusplatz 10/11, 04109 Leipzig, Germany
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly
diluted sites or a quasi-periodicity of the lattice, for altering the critical
behavior of a coupled statistical mechanics system. We investigate the
applicability of this type of criterion to the case of spin variables coupled
to random lattices. Their aptitude to alter critical behavior depends
on the degree of spatial correlations present, which is quantified by a
wandering exponent. We consider the cases of Poissonian random graphs
resulting from the Voronoï-Delaunay construction and of planar, “fat” φ 3
DY 17 Fluids II
Feynman diagrams and precisely determine their wandering exponents.
The resulting predictions are compared to various exact and numerical
results for the Potts model coupled to these quenched ensembles of random
graphs.
[1] W. Janke and M. Weigel, The Harris-Luck criterion for random lattices,
Leipzig preprint LU-ITP 2003/021, e-print cond-mat/0310269.
DY 16.4 Mo 17:30 H2
On the Structure of Microcanonical Entropy Surfaces of Finite
Systems — •Hans Behringer — Institut für Theoretische Physik
I, Universität Erlangen-Nürnberg, Staudtstrasse 7, D - 91058 Erlangen,
Germany
The basic quantity in the microcanonical approach to statistical properties
of magnetic systems is the entropy S(E, M) = ln Ω(E, M) where
Ω(E, M) is the density of states. The spontaneous magnetization and
the response functions like the magnetic susceptibility and the specific
heat are obtained from the curvature properties of the entropy surface.
Even for finite system sizes they show features which are typical of phase
transitions. The appearance of classical exponents characterising the singularities
of thermostatic quantities of finite systems can be understood
from the analyticity of the entropy surface. Symmetry properties of the
microcanonical entropy are deduced directly from the invariance group
of the Hamiltonian. These properties allow further general statements on
the global structure of the entropy surface.
[1] H.Behringer, Symmetries of Microcanonical Entropy Surfaces, J.
Phys. A: Math. Gen. 36, 8739 (2003)
[2] H.Behringer, Microcanonical Entropy for Small Magnetisations, to
appear in J. Phys. A, preprint cond-mat/0311211
DY 16.5 Mo 17:45 H2
Performance Limitations of Flat Histogram Methods — •Simon
Trebst — Theoretische Physik, Eidgenoessische Technische Hochschule
Zuerich, CH-8093 Zuerich, Schweiz
We determine the optimal scaling of local-update flat-histogram methods
with system size by using a perfect flat-histogram scheme based upon
the exact density of states of 2D Ising models. The typical tunneling time
needed to sample the entire bandwidth does not scale with the number of
spins N as the minimal N 2 of an unbiased random walk in energy space.
While the scaling is power law for the ferromagnetic and fully frustrated
Ising model, for the ±J nearest-neighbor spin glass the distribution of
tunneling times is governed by a fat-tailed Fréchet extremal value distribution
that obeys exponential scaling. The shape parameter of these
distributions furthermore indicate that statistical sample means become
ill-defined already for moderate system sizes within these complex energy
landscapes. We discuss ways to overcome these limitations by improved
sampling mechanisms.
References: P.Dayal, S.Trebst, S.Wessel, D.Wurtz, M.Troyer,
S.Sabhapandit, S.N.Coppersmith, cond-mat/0306106, accepted for publication
in Phys. Rev. Lett.
Zeit: Montag 16:30–18:00 Raum: H3
DY 17.1 Mo 16:30 H3
Raumzeitliches Verhalten zweier nichtmischbarer
Flüssigkeitsfilme — •Domnic Merkt 1 , Andreij Pototsky 1 ,
Michael Bestehorn 1 und Uwe Thiele 2 — 1 Erich-Weinert-Strasse
1, 03046 Cottbus — 2 Nöthnitzer Strasse 38, 01187 Dresden
Zwei nichtmischbare, dünne Flüssigkeitsschichten, begrenzt durch feste
Ränder, können durch eine Evolutionsgleichung der Grenzfläche
der beiden Flüssigkeiten beschrieben werden (Schmiermittelnäherung).
Die Mobilitäten dieser Gleichung haben eine grundlegend andere und
kompliziertere Form als die Mobilitäten der ausführlich untersuchten
Dünnfilmgleichungen eines einzelnen Fluids. Die Möglichkeiten auftretender
Instabilitäten werden durch diese Mobilitäten, bedingt durch Materi-
alparamter, vergrössert. Es wird der Einfluss verschiedener, auf das System
wirkender Kräfte vorgestellt (Gravitation, Marangonieffekt). Neben
linearen Untersuchungen werden auch Langzeitentwicklungen der vollen
nichtlinearen Gleichung gezeigt.
DY 17.2 Mo 16:45 H3
Shape transformations of fluid micrustructures induced by electrowetting
— •Anke Klingner, Renate Nikopoulos, Juergen
Buehrle, Stephan Herminghaus und Frieder Mugele — Universitaet
Ulm, Abt. Angewandte Physik, Albert-Einstein-Allee 11, D-89081
Ulm
A growing number of applied sciences as DNA analysis and proteomics
are in need of microfluidic devices, which are able to control small