论文标题
ISING，顶点和二聚体模型的关键线的通用性
Universality for critical lines for Ising, Vertex and Dimer models
论文作者
论文摘要
在平面晶格统计力学模型中，例如与四分之一相互作用，顶点和二聚体模型耦合，这些指数取决于所有汉密尔顿的细节。这在重新归一化组语言中对应于固定点的一行。预计一种普遍性的一种形式，这意味着所有指数都可以用一个单个单个的“ Kadanoff”关系来表达。该猜想最近已建立，我们在这里回顾了证明的关键步骤，该证明是通过严格的重新归一化方法获得的，而无需对模型的溶解度有效。指数通过耦合中的收敛序列表示，并且由于新兴的手性对称性引起的一系列取消，因此证明扩展的缩放关系被证明是正确的。
In planar lattice statistical mechanics models like coupled Ising with quartic interactions, vertex and dimer models, the exponents depend on all the Hamiltonian details. This corresponds, in the Renormalization Group language, to a line of fixed points. A form of universality is expected to hold, implying that all the exponents can be expressed by exact "Kadanoff" relations in terms of a single one of them. This conjecture has been recently established and we review here the key step of the proof, obtained by rigorous Renormalization Group methods and valid irrespectively on the solvability of the model. The exponents are expressed by convergent series in the coupling and, thanks to a set of cancellations due to emerging chiral symmetries, the extended scaling relations are proven to be true.
