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Absence of self-averaging in global optimization problems

Alex Hansen and János Kertész
Phys. Rev. E 53, R5541(R) – Published 1 June 1996
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Abstract

We study the distribution of (1+1)-dimensional self-affine lines resulting from the zero-temperature directed polymer in a random medium or from critical directed percolation problems. The related amplitude ratios depend on whether the finite size scaling statistics is made over finite segments of the infinite objects or over the finite objects of diverging size. As a by-product we obtain the correction to scaling exponents for the finite size scaling of the distribution functions.

  • Received 31 January 1996

DOI:https://doi.org/10.1103/PhysRevE.53.R5541

©1996 American Physical Society

Authors & Affiliations

Alex Hansen* and János Kertész

  • Höchstleistungsrechenzentrum, Kernforschungsanlage Jülich, D-52425 Jülich, Germany

  • *Permanent address: Department of Physics, Norwegian University of Science and Technology, N-7034 Trondheim, Norway. Electronic address: Alex.Hansen@phys.unit.no
  • Permanent address: Department of Theoretical Physics, Institute of Physics, Technical University of Budapest, H-1111 Budapest, Hungary. Electronic address: kertesz@phy.bme.hu

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Issue

Vol. 53, Iss. 6 — June 1996

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