2004
DOI: 10.1140/epjb/e2004-00329-0
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Large deviations in spin-glass ground-state energies

Abstract: Abstract. The ground-state energy E0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to infinity. In most cases, the behavior can be understood qualitatively, in particular with the help of semi-analytical results for hierarchical lattices. Particular attention is paid to the Sherrington-Kirkpatrick model; after comparing to the Tracy-Widom distribution which follows from the spherical approximation, … Show more

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Cited by 37 publications
(93 citation statements)
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“…If the energies within that spectrum are uncorrelated, it can be shown that the PDF for e 0 is among one of only a few universal functions. This extreme-value statistics of the ground states has been pointed out in Ref.[5] and has received considerable attention recently [6,7,8,9]. For instance, if the sum for H in Eq.…”
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confidence: 69%
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“…If the energies within that spectrum are uncorrelated, it can be shown that the PDF for e 0 is among one of only a few universal functions. This extreme-value statistics of the ground states has been pointed out in Ref.[5] and has received considerable attention recently [6,7,8,9]. For instance, if the sum for H in Eq.…”
mentioning
confidence: 69%
“…Indeed, in mean-field models Refs. [6,7,9,11] find numerically a highly skewed PDF for e 0 which does not fit to the Gumbel distribution in Eq. (3) for an m = 1-lowest value.…”
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confidence: 94%
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“…We compared the sample complexity with the numerical data at zero temperature of Ref. [5] as a function ∆e and find a very good agreement. For each N we have plotted ∆Σ N = ln(P (∆e N )/N 5/6 )/N with ∆e N = e − e N (the average energy at size N ): we put the N 5/6 factor in the definition so that that ∆Σ goes to a constant for ∆e N = 0.…”
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confidence: 74%
“…Indeed based on Kondor's result it was argued in [2] that the small deviations of the free energy per spin from its mean scale as N −5/6 . This prediction has been put to test in a series of numerical works [3,4,5,6,7,8,9] and although all estimates are smaller than 5/6 nobody has claimed that this value is definitively ruled out. However it was difficult to test the theory in absence of a quantitative prediction (the only prediction being on the exponent, a quantity that it is rather difficult to measure in a reliable way).…”
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confidence: 99%