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Hysteretic optimization for spin glasses

B Gonçalves and S Boettcher

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The recently proposed hysteretic optimization (HO) procedure is applied to the 1D Ising spin chain with long range interactions. To study its effectiveness, the quality of ground state energies found as a function of the distance dependence exponent, σ, is assessed. It is found that the transition from an infinite range to a long range interaction at σ = 0.5 is accompanied by a sharp decrease in the performance. The transition is signaled by a change in the scaling behavior of the average avalanche size observed during the hysteresis process. This indicates that HO requires the system to be infinite range, with a high degree of interconnectivity between variables leading to large avalanches, in order to function properly. An analysis of the way autocorrelations evolve during the optimization procedure confirm that the search of phase space is less efficient, with the system becoming effectively stuck in suboptimal configurations much earlier. These observations explain the poor performance that HO obtained for the Edwards–Anderson spin glass on finite-dimensional lattices, and suggest that its usefulness might be limited in many combinatorial optimization problems.


Keywords

analysis of algorithms

spin glasses (theory)

avalanches (theory)

robust and stochastic optimization

 

E-print Number: 0710.2138

Cited: by |

Refers: to

PACS

75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects

75.10.Pq Spin chain models

75.10.Hk Classical spin models

75.50.Lk Spin glasses and other random magnets

75.10.Nr Spin-glass and other random models

MSC

82C44 Dynamics of disordered systems (random Ising systems, etc.)

82D30 Random media, disordered materials (including liquid crystals and spin glasses)

Subjects

Condensed matter: electrical, magnetic and optical

Dates

Issue 01 (January 2008)

Received 10 October 2007, accepted for publication 4 December 2007

Published 3 January 2008



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