On the energy landscape of spherical spin glasses

Antonio Auffinger; Wei Kuo Chen

doi:10.1016/j.aim.2018.03.028

On the energy landscape of spherical spin glasses

Antonio Auffinger, Wei Kuo Chen

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. For these measures, we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other. In sharp contrast, we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy.

Original language	English (US)
Pages (from-to)	553-588
Number of pages	36
Journal	Advances in Mathematics
Volume	330
DOIs	https://doi.org/10.1016/j.aim.2018.03.028
State	Published - May 25 2018

Bibliographical note

Funding Information:
Research of Antonio Auffinger was partially supported by NSF Grant CAREER DMS-1653552 and NSF Grant DMS-1517894. Research of Wei-Kuo Chen was partially supported by NSF grant DMS-1642207 and Hong Kong Research Grants Council GRF-14302515.

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Energy landscapes
Parisi formula
Replica symmetry breaking
Spherical spin glasses

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title = "On the energy landscape of spherical spin glasses",

abstract = "We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. For these measures, we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other. In sharp contrast, we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy.",

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N2 - We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. For these measures, we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other. In sharp contrast, we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy.

AB - We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. For these measures, we show that any two nonparallel spin configurations around the maximum energy are asymptotically orthogonal to each other. In sharp contrast, we study models with full replica symmetry breaking and show that all possible values of the asymptotic distance are attained near the maximum energy.

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On the energy landscape of spherical spin glasses

Abstract

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Keywords

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