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arXiv · 1802.02991

Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperature

Antonio Auffinger·Qiang Zeng
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Abstract

We provide the first examples of two-step replica symmetry breaking (2-RSB) models for the spherical mixed p-spin glass at zero temperature. Precisely, we show that for a certain class of mixtures, the Parisi measure at zero temperature is purely atomic and has exactly three distinct points in its support. We then derive a few consequences for the topology of the random landscape in these cases. Our main result also provides a negative answer to a question raised in 2011 by Auffinger and Ben Arous about the classification of pure-like and full mixture models.

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Antonio Auffinger, Qiang Zeng. 2018-02-08. Existence of two-step replica symmetry breaking for the spherical mixed p-spin glass at zero temperature. https://doi.org/10.1007/s00220-018-3252-3

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