Comparing extremal and thermal Explorations of Energy Landscapes

Details Comparing extremal and thermal Explorations of Energy Landscapes Comparing extremal and thermal Explorations of Energy Landscapes

2004-06-23

arxiv.org/abs/cond-mat/0406543v2

European Physics Journal B 44, 317-326 (2005).

Physics

Condensed Matter

Disordered Systems and Neural Networks

RevTex4, 11 pages, 24 postscript figures included, to appear in EPJB; see http://www.physics.emory.edu/faculty/boettcher/ for

Scientific paper

10.1140/epjb/e2005-00131-6

Using a non-thermal local search, called Extremal Optimization (EO), in conjunction with a recently developed scheme for classifying the valley structure of complex systems, we analyze a short-range spin glass. In comparison with earlier studies using a thermal algorithm with detailed balance, we determine which features of the landscape are algorithm dependent and which are inherently geometrical. Apparently a characteristic for any local search in complex energy landscapes, the time series of successive energy records found by EO also is characterized approximately by a log-Poisson statistics. Differences in the results provide additional insights into the performance of EO. In contrast with a thermal search, the extremal search visits dramatically higher energies while returning to more widely separated low-energy configurations. Two important properties of the energy landscape are independent of either algorithm: first, to find lower energy records, progressively higher energy barriers need to be overcome. Second, the Hamming distance between two consecutive low-energy records is linearly related to the height of the intervening barrier.

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