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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 62 (1991), S. 1-19 
    ISSN: 1572-9613
    Keywords: Spin glasses ; order parameter ; self-averaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove that ifĤ N is the Sherrington-Kirkpatrick (SK) Hamiltonian and the quantity $$\bar q_N = N^{ - 1} \sum \left\langle {S_l } \right\rangle _H^2 $$ converges in the variance to a nonrandom limit asN→∞, then the mean free energy of the model converges to the expression obtained by SK. Since this expression is known not to be correct in the low-temperature region, our result implies the “non-self-averaging” of the order parameter of the SK model. This fact is an important ingredient of the Parisi theory, which is widely believed to be exact. We also prove that the variance of the free energy of the SK model converges to zero asN→∞, i.e., the free energy has the self-averaging property.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 72 (1993), S. 113-125 
    ISSN: 1572-9613
    Keywords: Free energy ; overlaps ; self-averaging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that in the limitp→ ∞,N → 0,α=p/N → 0 the limit free energy of the Hopfield model equals in probability the Curie-Weiss free energy. We prove also that the free energy of the Hopfield model is self-averaging for any finite ∞.
    Type of Medium: Electronic Resource
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  • 3
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 43 (2013): 905–919, doi:10.1175/JPO-D-12-0150.1.
    Description: Interactions between vortices and a shelfbreak current are investigated, with particular attention to the exchange of waters between the continental shelf and slope. The nonlinear, three-dimensional interaction between an anticyclonic vortex and the shelfbreak current is studied in the laboratory while varying the ratio ε of the maximum azimuthal velocity in the vortex to the maximum alongshelf velocity in the shelfbreak current. Strong interactions between the shelfbreak current and the vortex are observed when ε 〉 1; weak interactions are found when ε 〈 1. When the anticyclonic vortex comes in contact with the shelfbreak front during a strong interaction, a streamer of shelf water is drawn offshore and wraps anticyclonically around the vortex. Measurements of the offshore transport and identification of the particle trajectories in the shelfbreak current drawn offshore from the vortex allow quantification of the fraction of the shelfbreak current that is deflected onto the slope; this fraction increases for increasing values of ε. Experimental results in the laboratory are strikingly similar to results obtained from observations in the Middle Atlantic Bight (MAB); after proper scaling, measurements of offshore transport and offshore displacement of shelf water for vortices in the MAB that span a range of values of ε agree well with laboratory predictions.
    Description: Laboratory work was supported by the National Science Foundation through Grant OCE- 0081756. Glider observations in March–April 2006 were supported by the National Science Foundation through Grant OCE-0220769. Glider observations in July– October 2007 were supported by a grant from Raytheon. RET was supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Cooperative Institute for the North Atlantic Region. The REMUS observations were funded by the Office of Naval Research. GGG was supported by the National Science Foundation through Grant OCE-1129125 for analysis and writing.
    Description: 2013-11-01
    Keywords: Continental shelf/slope ; Eddies ; Fronts ; Transport ; Laboratory/physical models
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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