Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Complex energy landscapes (addendum to SYEL)

DY 3.4: Talk

Monday, March 22, 2010, 14:45–15:00, H42

A dedicated algorithm for calculating ground states for the triangular random bond Ising model — •Oliver Melchert and Alexander K. Hartmann — Institut für Physik, Universität Oldenburg, Carl-von-Ossietzky Str. 9-11, 26111 Oldenburg, Germany

Triggered by the exchange of ideas between computer science and theoretical physics, several disordered systems with complex energy landscapes can now be analyzed numerically exact through computer simulations [1] by using fast combinatorial optimization algorithms.

For example, the ground-state problem for the planar 2d random bond Ising model (RBIM) can be mapped to an auxiliary minimum-weight perfect matching problem, solvable in polynomial time. Consequently, the GS properties as well as minimum-energy domain wall (MEDW) excitations can be analyzed for large systems [2].

Here, we introduce a dedicated algorithm for the 2d RBIM on planar triangular lattices that improves on the running time of existing algorithms. Further, we investigate the critical behavior of the corresponding T=0 ferromagnet to spin-glass transition, signaled by a breakdown of the magnetization, using finite-size scaling analyses of the MEDW excitation energy. Finally, we contrast our numerical results with previous simulations and presumably exact results [3].
 A.K. Hartmann, Practical Guide to Computer Simulations, World Scientific (2009)
 OM, and A.K. Hartmann, Phys. Rev. B 79 (2009) 184402
 J. Bendisch, Physica A 245 (1997) 560