Comparing extremal and thermal Explorations of Energy Landscapes

TL;DR

This paper compares extremal and thermal exploration methods of energy landscapes in spin glasses, revealing algorithm-dependent features and universal geometrical properties through analysis of energy records and barriers.

Contribution

It introduces a comparative analysis of extremal and thermal algorithms on energy landscapes, highlighting their differences and universal properties in complex systems.

Findings

Extremal Optimization visits higher energies and more separated low-energy states than thermal algorithms.

Energy barriers to lower energy records increase with the energy level.

Hamming distance between low-energy states is linearly related to barrier height.

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 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.