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DY: Fachverband Dynamik und Statistische Physik
DY 10: Posters I
DY 10.45: Poster
Monday, March 14, 2011, 17:00–19:00, P4
Drawing energy landscapes of spin glasses — •Karsten Looschen and Alexander Hartmann — Carl von Ossietzky Universität Oldenburg, Institut für Physik, D-26111 Oldenburg
The rough energy landscape of a spin glass is regarded as one of its main features, but how does it look like? Often a schematical sketch with a one dimensional arrangement of states is drawn, however for a spin glass of N Ising spins the energy landscape consists of 2N states in a N-dimensional space. We propose different algorithms to systematically retrieve a meaningful arrangement of states.
Since enumeration of all states is impossible for all but very small systems, some (103 - 105) states are statistically sampled. Efficient hierarchical clustering algorithms based on a similarity measure for the sampled states can be used to alleviate the problem of high dimensionality. Leafs which are near each other in the resulting tree represent states with high similarity. This feature of the tree enables a simple plot of the energy landscape with a one dimensional arrangement of states.
The three dimensional Edwards-Anderson ± J spin glass with bond strengths −J (probability p) and +J (probability 1−p) is examined. This system is a spin glass if 0.23 < p < 0.77 and a ferromagnet else. Graphical representations of its energy landscape are retrieved and the “roughness” is characterized as a function of p.