非均匀非对称蝴蝶结晶格的Potts临界前沿
Potts critical frontiers of inhomogeneous and asymmetric bow-tie lattices
摘要：
研究了具有完全非均匀耦合常数的二维蝴蝶结晶格上Potts模型的临界前沿。一般来说，要精确地找到Potts临界前沿，其基础格必须是3-一致超图。更一般的一类格是4-一致格，单位晶胞包含在四个边界顶点内。我们证明，在某些情况下，这种晶格可以分解成三角形细胞，并解决了使用修改的标准技术。这导致了在各种晶格上的精确的非均匀Potts临界边界，例如具有五种不同耦合的蝴蝶结晶格，以及非对称蝴蝶结晶格的临界点。
英文摘要：
We study the critical frontiers of the Potts model on two-dimensional bow-tie lattices with fully inhomogeneous coupling constants. Generally, for the Potts critical frontier to be found exactly, the underlying lattice must be a 3-uniform hypergraph. A more general class of lattices are the 4-uniform ones, with unit cells contained within four boundary vertices. We demonstrate that in some cases, such lattices can be decomposed into triangular cells, and solved using a modification of standard techniques. This leads to the exact inhomogeneous Potts critical frontiers on various lattices, such as the bow-tie lattice with five different couplings, and critical points for asymmetric bow-tie lattices.
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