Dresden 2014 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.
DY 41.43: Poster
Donnerstag, 3. April 2014, 17:00–19:00, P3
On the uniform sampling of ground states in the 2D ± J Ising spin glass model — •Hamid Khoshbakht1,2 and Martin Weigel1,2 — 1Institut für Physik, Johannes Gutenberg-Universitaät Mainz, D-55099 Minz, Germany — 2Applied Mathematics Research Centre, Coventry University, Coventry, CV1 5FB, UK
It is well known that the Edwards-Anderson Ising spin glass with discrete coupling distribution results in an extensive ground-state degeneracy. As the number of ground states hence grows exponentially with system size L, an exact enumeration is not practical, except for very small systems. This even applies to the otherwise well tractable model in two dimensions. There, exact ground states can be generated in polynomial time using one of several known mappings to minimum-weight perfect matching problems. While the resulting algorithm can be modified to generate random ground states in the presence of degeneracies, these are not in general produced with uniform probabilities. Here, we introduce an approach that achieves approximate uniform sampling. The algorithm is based on a cluster analysis of connected domains of free spins resulting from inputs generated by the matching approach which are then used as state space for a suitably adapted Markov chain sampling.