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DY: Fachverband Dynamik und Statistische Physik
DY 13: Statistical Physics (general)
DY 13.6: Vortrag
Montag, 7. März 2016, 16:15–16:30, H48
Melting in 2D and a Fresh Perspective on Monte Carlo — •Sebastian Kapfer1 and Werner Krauth2 — 1Theoretische Physik 1, FAU Erlangen — 2LPS, Ecole Normale Superieure, Paris
The melting transition of two-dimensional solids has been the subject of continued research for more than fifty years, with the prevalent scenarios being the KTHNY theory of defect unbinding and a conventional first-order liquid/solid transition. For hard disks, the KTHNY scenario has recently been essentially confirmed, even though the liquid-hexatic step is of first order [1]. A key problem in these simulations are the large correlation lengths, which we tackle using a new rejection-free global-balance Monte Carlo algorithm [2].
We show that the hard disk result transfers to soft interactions with inverse power-law or Yukawa potentials [3]. The order of the liquid-hexatic step can be tuned from first-order to continuous by softening the potential. We show that there is always a hexatic phase separating the liquid and solid phases, and identify two regimes of the hexatic with vastly different correlation lengths.
The new algorithm is very versatile, and could also be applied to spin systems, polymers, path integral problems, etc. It can be augmented to treat long-range force laws such as Coulomb without any artificial truncation.
[1] E. P. Bernard, W. Krauth, Phys. Rev. Lett. 107, 155704 (2011). [2] M. Michel et al., J. Chem. Phys. 140, 054116 (2014). [3] S. C. Kapfer, W. Krauth, Phys. Rev. Lett. 114, 035702 (2015).