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We prove that the Parisi measure of the mixed p-spin model at zerotemperature has infinitely many points in its support. This establishesParisi's prediction that the functional order parameter of theSherrington-Kirkpatrick model is not a step function at zero temperature. As aconsequence, we show that the number of levels of broken replica symmetry inthe Parisi formula of the free energy diverges as the temperature goes to zero.

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