Boundary CFT and Tensor Network Approach to Surface Critical Phenomena of the Tricritical 3-State Potts model
Boundary CFT and Tensor Network Approach to Surface Critical Phenomena of the Tricritical 3-State Potts model
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DOI：
10.1007/s10955-021-02728-y
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发表时间：
2020-07
影响因子：
1.6
通讯作者：
Shumpei Iino
中科院分区：
文献类型：
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作者：
Shumpei Iino
二维经典系统的一维边有时会表现出惊人的丰富的相变和临界现象，特别是当体处于临界状态时。作为这样一个模型，我们研究了体积在三临界点调谐的三态稀Potts模型的表面临界行为。为了比以前的工作（Deng and Blöte，Phys Rev E 70：035107，2004; Phys Rev E 71：026109，2005）更精确地研究它，我们从边界共形场论（BCFT）的观点来分析它。Behrend等人（Nucl Phys B 579：707，2000）中讨论的最小BCFTs的共形边界条件的完整分类允许我们收集三临界3态Potts BCFT中的12个边界不动点。利用张量网络重整化方法，对三临界三态Potts模型的表面相图进行了详细的数值研究，发现通过控制外场和边界耦合强度，可以在晶格上实现12个边界不动点中的11个边界不动点.最后一个未找到的不动点将在参数空间中的物理合理区域之外，类似于三态Potts BCFT中的“新”边界条件。
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.