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Energy exponents and corrections to scaling in Ising spin glasses

Abstract : We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.
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https://hal.archives-ouvertes.fr/hal-00002269
Contributor : Claudine Le Vaou Connect in order to contact the contributor
Submitted on : Friday, January 28, 2005 - 4:28:32 PM
Last modification on : Friday, October 8, 2021 - 2:04:15 PM

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Jean-Philippe Bouchaud, Florent Krzakala, Olivier Martin. Energy exponents and corrections to scaling in Ising spin glasses. Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2003, 68, pp.224404. ⟨hal-00002269⟩

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