论文标题
弱非平面二聚体
Weakly non-planar dimers
论文作者
论文摘要
我们研究了二维但不是平面的两部分周期图上完全包装的二聚体配置（或完美匹配）的模型。该图是从$ \ Mathbb Z^2 $获得的，它增加了大量破坏平面性的额外边缘（但不是双方）。我们证明，如果非平面边缘的重量$λ$足够小，则具有$λ$依赖性振幅的大距离上适当定义的高度功能尺度，与二聚体二聚体相关性的异常指数相吻合。由于非计划，Kasteleyn的理论不适用：该模型不可集成。相反，我们将模型映射到Luttinger通用类中相互作用的晶格费米子的系统，然后我们通过费米金重新归一化组方法进行分析。
We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\mathbb Z^2$ via the addition of an extensive number of extra edges that break planarity (but not bipartiteness). We prove that, if the weight $λ$ of the non-planar edges is small enough, a suitably defined height function scales on large distances to the Gaussian Free Field with a $λ$-dependent amplitude, that coincides with the anomalous exponent of dimer-dimer correlations. Because of non-planarity, Kasteleyn's theory does not apply: the model is not integrable. Rather, we map the model to a system of interacting lattice fermions in the Luttinger universality class, which we then analyze via fermionic Renormalization Group methods.
