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The SK model is infinite step replica symmetry breaking at zero temperature

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arxiv 1703.06872 v2 pith:FZCUZAOC submitted 2017-03-20 math.PR math-phmath.MP

Antonio Auffinger , Wei-Kuo Chen , Qiang Zeng This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords temperaturezeromodelparisireplicastepsymmetrybreaking
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We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.

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  1. The Overlap Gap Property in Principal Submatrix Recovery

    math.PR 2019-08 accept novelty 7.0 of 10

    A sharp information-theoretic threshold for approximate recovery of a planted sparse submatrix is derived, and an overlap gap property is proved that blocks local MCMC algorithms in a conjecturally hard phase.

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