On properties of Parisi measures

Understand

We investigate the structure of Parisi measures, the functional order parameters of mixed p-spin models in mean field spin glasses.

• In the absence of external field, we prove that a Parisi measure satisfies the following properties.
• First, at all temperatures, the support of any Parisi measure contains the origin.
• If it contains an open interval, then the measure has a smooth density on this interval.