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PreprintCC BY 4.0arXiv

Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model

  • Yunhui Chen
  • Keaton Fierro
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Abstract

We study the limiting law of local field in the mean field Ghatak-Sherrington model with spin values {0,±1,…,± S} in the high-temperature regime. Using the cavity method and the quantitative overlap and self-overlap estimates of Sheng-Wu~\cite{SW24}, we prove a central limit theorem for the non-centered cavity field. As a result, we then identify the local field limiting law as a random finite mixture of Gaussian distributions. The proof is based on moment method and gives a quantitative error bound.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026limiting,
  title = {{Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model}},
  author = {Yunhui Chen and Keaton Fierro},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.10515},
  eprint = {2608.10515},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.10515},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model
AU  - Yunhui Chen
AU  - Keaton Fierro
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.10515
UR  - https://arxiv.org/abs/2608.10515
AB  - We study the limiting law of local field in the mean field Ghatak-Sherrington model with spin values {0,±1,…,± S} in the high-temperature regime. Using the cavity method and the quantitative overlap and self-overlap estimates of Sheng-Wu~\cite{SW24}, we prove a central limit theorem for the non-centered cavity field. As a result, we then identify the local field limiting law as a random finite mixture of Gaussian distributions. The proof is based on moment method and gives a quantitative error bound.
ER  -