Phase diagram and fluctuations in the cubic mean field Ising model
Abstract
We study the cubic mean field Ising model with three body and two body interactions and an external field. Our main result is a complete classification of the global maximizers of the variational pressure in the full three-parameter region (K,J,h)∈(0,∞)×ℝ2. We identify a coexistence surface with two nondegenerate global maximizers and a critical curve with a unique quartically degenerate maximizer; elsewhere the maximizer is unique and nondegenerate. This extends the phase diagrams previously obtained on two-parameter subfamilies \cite{CMO24,O24}. As applications of the general results in \cite{CR}, we give explicit magnetization fluctuation theorems and asymptotic distributions for one-parameter maximum likelihood estimators in the resulting regimes.
Related
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BibTeX
@misc{can2026phase,
title = {{Phase diagram and fluctuations in the cubic mean field Ising model}},
author = {Van Hao Can and Viet Tinh Dang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25653},
eprint = {2610.25653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25653},
}
RIS
TY - UNPB
TI - Phase diagram and fluctuations in the cubic mean field Ising model
AU - Van Hao Can
AU - Viet Tinh Dang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25653
UR - https://arxiv.org/abs/2610.25653
AB - We study the cubic mean field Ising model with three body and two body interactions and an external field. Our main result is a complete classification of the global maximizers of the variational pressure in the full three-parameter region (K,J,h)∈(0,∞)×ℝ^2. We identify a coexistence surface with two nondegenerate global maximizers and a critical curve with a unique quartically degenerate maximizer; elsewhere the maximizer is unique and nondegenerate. This extends the phase diagrams previously obtained on two-parameter subfamilies \cite{CMO24,O24}. As applications of the general results in \cite{CR}, we give explicit magnetization fluctuation theorems and asymptotic distributions for one-parameter maximum likelihood estimators in the resulting regimes.
ER -