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DY: Dynamik und Statistische Physik

DY 16: Phase Transitions

DY 16.2: Vortrag

Montag, 8. März 2004, 17:00–17:15, 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).