Long range order for three-dimensional random field Ising model throughout the entire low temperature regime

• 成果类型: Article
• 署名作者: Ding, Jian; Liu, Yu; Xia, Aoteng
• 署名单位: Peking University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01283-z
• 发表日期: 2024
• 页码: 247-281
• 关键词: phase-transition; large deviations; surface-tension; monte-carlo; percolation; state; decay

摘要

For d >= 3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d\geq 3$\end{document}, we study the Ising model on Zd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{Z}<^>{d}$\end{document} with random field given by {& varepsilon;hv:v is an element of Zd}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{\epsilon h_{v}: v\in \mathbb{Z}<^>{d}\}$\end{document} where hv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$h_{v}$\end{document}'s are independent normal variables with mean 0 and variance 1. We show that for any T