Year: 2026
Type: preprint
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 $(K,J,h)\in(0,\infty)\times\mathbb R^2$. 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.
Source: arXiv (Cornell University)
Authors: Can, Van Hao, Dang, Viet Tinh
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223033402