AI 中文总结
该研究关联高度函数模型与广义二维XY模型，通过广义环表示论证高度函数非定域性排除向列序参数指数衰减，推广了van Engelenburg等人的结果，并重新得到向列区域的存在性。
AI 中文摘要
我们将高度函数模型与一系列广义二维XY模型关联起来，并证明高度函数模型的非定域性排除了原始自旋模型中向列序参数的指数衰减。该论证基于一种广义环表示，其将两个面之间的高度差的方差与向列序参数关联起来，这推广了van Engelenburg和Lis（2023）的结果。这些模型的范围还包括Korshunov提出、Lee与Grinstein独立提出的广受研究的广义XY模型，其中相邻自旋铁磁相互作用，有利于平行排列，而向列型相互作用则有利于平行或反平行排列。此外，我们通过Pfister（1982）的经典比较论证，重新得到了向列区域的存在性。
英文摘要
We associate height function models to a range of generalized two-dimensional XY models and prove that delocalisation of the height function model rules out exponential decay of the nematic order parameter in the primal spin model. The argument is based on a generalized loop representation which relates the variance of a height difference between two faces to the nematic order parameter. This generalizes the results by van Engelenburg and Lis (2023). The range of models also includes the much-studied generalized XY model as proposed by Korshunov and independently by Lee and Grinstein, where neighbouring spins interact ferromagnetically favouring parallel alignment and nematically favouring parallel or antiparallel alignment. Moreover, we recover the existence of a nematic region by a classical comparison argument of Pfister (1982).
Comments27 pages; comments welcome
