Overlap structure of mixed even $p$-spin models

We identify the limiting overlap structure of mixed even $p$-spin models, including the Sherrington-Kirkpatrick model, at every fixed deterministic external field. In particular, we show that the disorder-averaged distribution of the overlap, or its absolute value at zero field, converges to the Parisi measure. We identify the full limiting array using the overlap array of the associated Ruelle probability cascade. We also establish the corresponding Ghirlanda-Guerra identities and determine the limiting law of the quenched overlap distribution. For the zero-field Sherrington-Kirkpatrick model, we additionally prove temperature chaos at every pair of distinct nonnegative inverse temperatures.