摘要
本文目标是探讨统计物理的核心课题—相变现象.为此,需要发展已有的或寻找新的数学工具.重点在于刻画各种稳定性的速度.主要内容有耦合与距离方法及遍历性蕴含关系图,各种遍历性的显式判断标准与一种格子量子场模型,一维情形对偶变分公式、统一基本估计与Hardy不等式.
The goal of the paper is to explore the core issue of statistical physics-The phenomenon of phase transition.To do this,we need to develop some existing ones or?nd new mathematical tools,and the emphasis is on the speed at which we can characterize various stabilities.The main contents are as follows:the coupling and distance methods and ergodic implication diagram,explicit criteria of various ergodicity and a lattice quantum?eld model,one-dimensional dual variational formulas,uni?ed basic estimates and Hardy-inequality.
出处
《中国科学：数学》
CSCD
北大核心
2019年第3期327-338,共12页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11771046)资助项目
