发表机构
Université de Lorraine – CNRS; Albert-Ludwigs-Universität Freiburg; Islamic University of Gaza; Northumbria University（洛林大学–法国国家科学研究中心; 弗赖堡大学; 加沙伊斯兰大学; 诺森比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将平均场理论应用于量子相变领域，以伊辛模型和布伦-卡佩尔模型为研究对象，阐明该方法在零温度量子相变中的应用，补充其在量子相变研究中的应用场景。
AI 中文摘要
平均场理论是描述相变的广泛使用的近似方法，在上临界维度以上尤为有效，其起源可追溯到液-气相变的范德瓦尔斯理论以及顺磁-铁磁相变的外斯分子场理论。不过，是列夫·D·朗道提出了适用于一大类物理系统的统一通用框架。平均场方法通常忽略热涨落，这在许多经典场景中是合理假设，但它在零温度下的量子相变中的应用较少见。本短篇教学论文旨在探究并阐明平均场方法在不太熟悉的量子相变领域的应用，具体考虑伊辛模型和布伦-卡佩尔模型。
英文摘要
Mean-field theory is a widely used approximation for describing phase transitions, particularly effective above the upper critical dimension. Its origins can be traced back to the van der Waals theory of the liquid-gas transition and Weiss's molecular field theory of the paramagnetic-ferromagnetic transition. However, it was Lev D. Landau who provided a unifying and general framework applicable to a broad class of physical systems. The mean-field approach typically involves neglecting thermal fluctuations, which is a reasonable assumption in many classical contexts. However, its application to quantum phase transitions at zero temperature is less common. The aim of this short pedagogical paper is to explore and clarify the use of the mean-field approach in the less familiar domain of quantum phase transitions. We specifically consider the Ising model and the Blume-Capel model.
