由于体内关联函数和表面关联函数的共同作用，表面临界现象比体临界现象更加丰富多彩。在拓扑量子相变研究的推动下，近年来对量子磁性系统的表面临界行为的研究取得了一些突破，发现了反常的量子表面临界行为，比如对通常标度律的违背等，目前对此并没有很好的理解；对表面临界现象的认识亟待进一步加深。基于此，本项目将对一系列经典和量子格点模型的表面临界现象开展研究，着力于探索以下科学问题：（1）进一步探索量子表面临界现象的反常之处，寻找更多的违背标度律的表面临界现象，并揭示其共性特征，同时利用图形表象发掘经典模型中新的表面临界现象，借助经典与量子对比，理解标度反常的物理根源；（2）研究体相变为非Ginzburg-Landau范式情况下的量子表面临界现象；（3）探索“拓扑表面临界现象”的新奇之处。本项目的实施将加深对表面临界现象的理解，并为其开拓新的研究方向。

Surface critical phenomena are more colorful than bulk critical phenomena due to the interaction of bulk correlation function and surface correlation function. Driven by the study of topological quantum phase transition, some breakthroughs have been made in the study of surface critical behavior of quantum magnetic systems in recent years, and abnormal quantum surface critical behavior has been discovered, such as the violation of the usual scaling law, which is not well understood at present. The understanding of surface critical phenomena urgently needs to be further deepened. Based on this, this project will study the surface critical phenomena of a series of classical and quantum lattice models, focusing on the following scientific issues: (1) Further exploring the anomalies of quantum surface critical phenomena, finding more surface critical phenomena that violate the scaling law, and revealing their common characteristics; in addition, we will explore new surface critical phenomena in classical models by using graphical representation; with the help of classical and quantum comparison, we can understand the physical origin of scaling anomaly; (2) Studying the quantum surface critical phenomena in the case of non-Ginzburg-Landau paradigm of bulk transition; (3) Exploring the novelty of "topological surface critical phenomena". The implementation of this project will deepen the understanding of surface critical phenomena and open up new research directions for it.