FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2093339680> ?p ?o ?g. }

• W2093339680 abstract "Parisi's formal replica-symmetry-breaking (RSB) scheme for mean-field spin glasses has long been interpreted in terms of many pure states organized ultrametrically. However, the early version of this interpretation, as applied to the short-range Edwards-Anderson model, runs into problems because as shown by Newman and Stein (NS) it does not allow for chaotic size dependence, and predicts non-self-averaging that cannot occur. NS proposed the concept of the metastate (a probability distribution over infinite-size Gibbs states in a given sample that captures the effects of chaotic size dependence) and a nonstandard interpretation of the RSB results in which the metastate is nontrivial and is responsible for what was called non-self-averaging. In this picture, each state drawn from the metastate has the ultrametric properties of the old theory, but when the state is averaged using the metastate, the resulting mixed state has little structure. This picture was constructed so as to agree both with the earlier RSB results and with rigorous results. Here we use the effective field theory of RSB, in conjunction with the rigorous definitions of pure states and the metastate in infinite-size systems, to show that the nonstandard picture follows directly from the RSB mean-field theory. In addition, the metastate-averaged state possesses power-law correlations throughout the low-temperature phase; the corresponding exponent $ensuremath{zeta}$ takes the value 4 according to the field theory in high dimensions $d$, and describes the effective fractal dimension of clusters of spins. Further, the logarithm of the number of pure states in the decomposition of the metastate-averaged state that can be distinguished if only correlations in a window of size $W$ can be observed is of order ${W}^{densuremath{-}ensuremath{zeta}}$. These results extend the nonstandard picture quantitatively; we show that arguments against this scenario are inconclusive. More generally, in terms of Parisi's function $q(x)$, if $q(0)ensuremath{ne}{ensuremath{int}}_{0}^{1}dxphantom{rule{0.16em}{0ex}}q(x)$, then the metastate is nontrivial. In an Appendix, we also prove rigorously that the metastate-averaged state of the Sherrington-Kirkpatrick model is a uniform distribution on all spin configurations at all temperatures." @default.
• W2093339680 created "2016-06-24" @default.
• W2093339680 creator A5089808487 @default.
• W2093339680 date "2014-09-30" @default.
• W2093339680 modified "2023-10-18" @default.
• W2093339680 title "Short-range Ising spin glasses: The metastate interpretation of replica symmetry breaking" @default.
• W2093339680 cites W142487310 @default.
• W2093339680 cites W1495483394 @default.
• W2093339680 cites W1566060636 @default.
• W2093339680 cites W1569502688 @default.
• W2093339680 cites W1621963753 @default.
• W2093339680 cites W1732959709 @default.
• W2093339680 cites W1839269833 @default.
• W2093339680 cites W1963974922 @default.
• W2093339680 cites W1964159836 @default.
• W2093339680 cites W1966756028 @default.
• W2093339680 cites W1967084746 @default.
• W2093339680 cites W1973149840 @default.
• W2093339680 cites W1974572752 @default.
• W2093339680 cites W1975633702 @default.
• W2093339680 cites W1977549881 @default.
• W2093339680 cites W1982540327 @default.
• W2093339680 cites W1983020781 @default.
• W2093339680 cites W1985868645 @default.
• W2093339680 cites W1989702934 @default.
• W2093339680 cites W1990609584 @default.
• W2093339680 cites W1990755770 @default.
• W2093339680 cites W1990869101 @default.
• W2093339680 cites W1991904924 @default.
• W2093339680 cites W1992888030 @default.
• W2093339680 cites W1994001390 @default.
• W2093339680 cites W1995453127 @default.
• W2093339680 cites W1995801396 @default.
• W2093339680 cites W1997627815 @default.
• W2093339680 cites W2000449275 @default.
• W2093339680 cites W2002961206 @default.
• W2093339680 cites W2003678860 @default.
• W2093339680 cites W2006065897 @default.
• W2093339680 cites W2007480625 @default.
• W2093339680 cites W2011691684 @default.
• W2093339680 cites W2013520638 @default.
• W2093339680 cites W2013911361 @default.
• W2093339680 cites W2018415308 @default.
• W2093339680 cites W2021901382 @default.
• W2093339680 cites W2022714446 @default.
• W2093339680 cites W2022750082 @default.
• W2093339680 cites W2022820481 @default.
• W2093339680 cites W2023360441 @default.
• W2093339680 cites W2026846516 @default.
• W2093339680 cites W2036649439 @default.
• W2093339680 cites W2044139214 @default.
• W2093339680 cites W2044771296 @default.
• W2093339680 cites W2045288264 @default.
• W2093339680 cites W2047900759 @default.
• W2093339680 cites W2051401045 @default.
• W2093339680 cites W2055306805 @default.
• W2093339680 cites W2055405136 @default.
• W2093339680 cites W2059775469 @default.
• W2093339680 cites W2061706463 @default.
• W2093339680 cites W2063056171 @default.
• W2093339680 cites W2065264986 @default.
• W2093339680 cites W2066267336 @default.
• W2093339680 cites W2066492114 @default.
• W2093339680 cites W2070795014 @default.
• W2093339680 cites W2071840807 @default.
• W2093339680 cites W2073499847 @default.
• W2093339680 cites W2074578227 @default.
• W2093339680 cites W2075982228 @default.
• W2093339680 cites W2077118989 @default.
• W2093339680 cites W2078220182 @default.
• W2093339680 cites W2082701217 @default.
• W2093339680 cites W2087009309 @default.
• W2093339680 cites W2087594794 @default.
• W2093339680 cites W2088431067 @default.
• W2093339680 cites W2088968225 @default.
• W2093339680 cites W2091971392 @default.
• W2093339680 cites W2095058792 @default.
• W2093339680 cites W2101936356 @default.
• W2093339680 cites W2106712492 @default.
• W2093339680 cites W2143247021 @default.
• W2093339680 cites W2161410247 @default.
• W2093339680 cites W2561442668 @default.
• W2093339680 cites W2566505556 @default.
• W2093339680 cites W2802739963 @default.
• W2093339680 cites W2963349778 @default.
• W2093339680 cites W3021923881 @default.
• W2093339680 cites W3098209433 @default.
• W2093339680 cites W3100332659 @default.
• W2093339680 cites W3104486028 @default.
• W2093339680 cites W3105546769 @default.
• W2093339680 cites W3161858595 @default.
• W2093339680 cites W4205240937 @default.
• W2093339680 cites W4205261783 @default.
• W2093339680 cites W4210422269 @default.
• W2093339680 cites W4231768793 @default.
• W2093339680 cites W4236318857 @default.
• W2093339680 cites W4238113606 @default.
• W2093339680 cites W4240189201 @default.
• W2093339680 cites W567708786 @default.
• W2093339680 cites W885353442 @default.

• next