https://doi.org/10.1140/epjb/e2005-00131-6
Comparing extremal and thermal explorations of energy landscapes
1
Physics Department, Emory University, Atlanta, Georgia
30322, USA
2
Theoretical Physics, Oxford University, 1 Keble Rd, Oxford OX1 3NP, UK
Corresponding author: a sboettc@emory.edu
Received:
23
June
2004
Revised:
8
December
2004
Published online:
28
April
2005
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 is also characterized approximately by a Poisson statistic with logarithmic time arguments. 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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 75.10.Nr – Spin-glass and other random models / 02.60.Pn – Numerical optimization
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005