Fluctuations in the Potts spin glass model at high temperature
Abstract
We study the fluctuations of the free energy of the Potts spin glass with κ colors at high temperature. The disorder is symmetric with unit variance and finite fourth moment. For configurations with a balanced, or nearly balanced, color profile, the log-partition function satisfies a central limit theorem whenever β2<αc(κ). Here καc(κ) is the critical inverse temperature of the Curie-Weiss-Potts model. A comparison of color profiles transfers this limit to the unconstrained model for β<βmax(κ), an explicit threshold. In the same range, the magnetizations of two replicas and their overlap matrix satisfy a joint quenched central limit theorem with independent Gaussian limits. The fourth cumulant of the disorder enters the limiting mean and variance explicitly.
Related
- Positive-temperature spin-glass order on the three-dimensional Migdal-Kadanoff lattice
- TAP equations for orthogonally invariant spin glasses at high temperature
- Ghirlanda-Guerra identities and cavity equations for diluted spin glass models
- Fluctuations of the Sherrington-Kirkpatrick free energy at critical temperature
- Towards the spin-glass transition in finite dimensions via blue percolation
BibTeX
@misc{dey2026fluctuations,
title = {{Fluctuations in the Potts spin glass model at high temperature}},
author = {Partha S. Dey and Taegu Kang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19356},
eprint = {2610.19356},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19356},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fluctuations in the Potts spin glass model at high temperature
AU - Partha S. Dey
AU - Taegu Kang
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19356
UR - https://arxiv.org/abs/2610.19356
AB - We study the fluctuations of the free energy of the Potts spin glass with κ colors at high temperature. The disorder is symmetric with unit variance and finite fourth moment. For configurations with a balanced, or nearly balanced, color profile, the log-partition function satisfies a central limit theorem whenever β^2<α_c(κ). Here κα_c(κ) is the critical inverse temperature of the Curie-Weiss-Potts model. A comparison of color profiles transfers this limit to the unconstrained model for β<β_max(κ), an explicit threshold. In the same range, the magnetizations of two replicas and their overlap matrix satisfy a joint quenched central limit theorem with independent Gaussian limits. The fourth cumulant of the disorder enters the limiting mean and variance explicitly.
ER -