Hysteretic Optimization For Spin Glasses

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dc.creatorGoncalves, B.
dc.creatorBoettcher, S.
dc.date2007-10-10
dc.date2007-12-10
dc.date.accessioned2026-07-07T08:56:59Z
dc.date.available2026-07-07T08:56:59Z
dc.descriptionThe 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 auto-correlations 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.
dc.description6 pages, 9 figures. To appear in JSTAT. Author website: http://www.bgoncalves.com
dc.identifierhttps://arxiv.org/abs/0710.2138
dc.identifierhttp://arxiv.org/abs/0710.2138
dc.identifierJ. Stat. Mech. (2008) P01003
dc.identifierdoi:10.1088/1742-5468/2008/01/P01003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146808
dc.subjectSoft Condensed Matter
dc.titleHysteretic Optimization For Spin Glasses
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