Eur. Phys. J. B 44, 317-326 (2005)
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

Abstract

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.