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.
Bibliographical noteFunding 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.
- Energy landscapes
- Parisi formula
- Replica symmetry breaking
- Spherical spin glasses