Local optima of the Sherrington-Kirkpatrick Hamiltonian
نویسندگان
چکیده
منابع مشابه
Local optima of the Sherrington-Kirkpatrick Hamiltonian
We study local optima of the Hamiltonian of the Sherrington-Kirkpatrick model. We compute the exponent of the expected number of local optima and determine the “typical” value of the Hamiltonian. *Supported by NSERC Discovery Grant 341845. †Supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. ‡Supported by the SpanishMinistry of Economy and Competitiveness, Gran...
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The Sherrington-Kirkpatrick (SK) model was introduced by David Sherrington and Scott Kirkpatrick in 1975 as a simple ‘solvable’ (in their words) model for spin-glasses. Spin-glasses are some type of magnetic alloys, and ‘solvable’ meant that the asymptotic free entropy density could be computed exactly. It turns out that the original SK solution was incorrect and in fact inconsistent (the autho...
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We present extended versions and give detailed proofs of results concerning percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems co...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2019
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.5020662