In this work, an exact renormalization group treatment of honeycomb lattice leading to an exact relation between the coupling strengths of the honeycomb and the triangular lattices is presented. Using the honeycomb and the triangular duality relation, the critical coupling values of honeycomb and triangular lattices are calculated exactly by the simultaneous solution of the renormalized relation and the duality relation, without using the so-called star-triangular transformation. Apparently, the obtained coupling relation is unique. It not only takes place the role of the star triangular relation, but it is also the only exact relation obtained from renormalization group theory other than the 1D Ising chain. An exact pair correlation function expression relating the nearest neighbors and the next nearest neighbor correlation functions are also obtained for the honeycomb lattice. Utilizing this correlation relation, an exact expression of the correlation length of the honeycomb lattice is calculated analytically for the coupling constant values less than the critical value in the realm of the scaling theory. The critical exponents ν and α are also calculated as ν = 1 and α = 0.

中文翻译：

---

二维非自对偶伊辛格：精确的重整化组处理

在这项工作中，提出了蜂窝晶格的精确重整化组处理，导致蜂窝和三角形晶格的耦合强度之间存在精确关系。利用蜂窝和三角对偶关系，通过重整化关系和对偶关系的联立解，精确计算出蜂窝和三角格的临界耦合值，而不使用所谓的星三角变换。显然，得到的耦合关系是唯一的。它不仅起到了星三角关系的作用，而且也是唯一从重整化群论中得到的除一维伊辛链之外的精确关系。对于蜂窝晶格，还获得了与最近邻和次最近邻相关函数相关的精确对相关函数表达式。利用该相关关系，对于小于标度理论领域中的临界值的耦合常数值，分析计算蜂窝晶格的相关长度的精确表达式。关键指数ν和α也计算为ν = 1和α = 0.