PreprintarXiv licencearXiv
Overlap structure of mixed even p-spin models
Abstract
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.
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BibTeX
@misc{aronow2026overlap,
title = {{Overlap structure of mixed even $p$-spin models}},
author = {P. M. Aronow and Patrick Lopatto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17442},
eprint = {2609.17442},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17442},
}
RIS
TY - UNPB
TI - Overlap structure of mixed even p-spin models
AU - P. M. Aronow
AU - Patrick Lopatto
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17442
UR - https://arxiv.org/abs/2609.17442
AB - 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.
ER -