One-dimensional edges of classical systems in two dimension sometimes show surprisingly rich phase transitions and critical phenomena, particularly when the bulk is at criticality. As such a model, we study the surface critical behavior of the 3-state dilute Potts model whose bulk is tuned at the tricritical point. To investigate it more precisely than in the previous works (Deng and Blöte, Phys Rev E 70:035107, 2004; Phys Rev E 71:026109, 2005), we analyze it from the viewpoint of the boundary conformal field theory (BCFT). The complete classification of the conformal boundary conditions for the minimal BCFTs discussed in Behrend et al. (Nucl Phys B 579:707, 2000) allows us to collect the twelve boundary fixed points in the tricritical 3-state Potts BCFT. Employing the tensor network renormalization method, we numerically study the surface phase diagram of the tricritical 3-state Potts model in detail, and reveal that the eleven boundary fixed points among the twelve can be realized on the lattice by controlling the external field and coupling strength at the boundary. The last unfound fixed point would be out of the physically sound region in the parameter space, similarly to the ‘new’ boundary condition in the 3-state Potts BCFT.

二维经典系统的一维边缘有时会显示出令人惊讶的丰富的相变和临界现象，尤其是当主体处于临界状态时。作为这样的模型，我们研究了三态稀Potts模型的表面临界行为，该模型的体积在三临界点进行了调整。为了比以前的工作（Deng和Blöte，Phys Rev E 70：035107，2004； Phys Rev E 71：026109，2005）更精确地进行研究，我们从边界共形场理论（BCFT）的角度对其进行了分析。Behrend等人讨论的最小BCFT的共形边界条件的完整分类。（Nucl Phys B 579：707，2000）使我们能够收集三临界三态Potts BCFT中的十二个边界固定点。使用张量网络重归一化方法，我们对三临界三态Potts模型的表面相图进行了数值研究，发现通过控制边界处的外场和耦合强度，可以在晶格上实现十二个中的十一个边界固定点。最后一个找不到的不动点将超出参数空间中的物理声音区域，类似于三态Potts BCFT中的“新”边界条件。