Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84511 Bratislava, Slovakia.
Phys Rev E. 2018 Jan;97(1-1):012108. doi: 10.1103/PhysRevE.97.012108.
The partition function of the symmetric (zero electric field) eight-vertex model on a square lattice can be formulated either in the original "electric" vertex format or in an equivalent "magnetic" Ising-spin format. In this paper, both electric and magnetic versions of the model are studied numerically by using the corner transfer matrix renormalization-group method which provides reliable data. The emphasis is put on the calculation of four specific critical exponents, related by two scaling relations, and of the central charge. The numerical method is first tested in the magnetic format, the obtained dependencies of critical exponents on the model's parameters agree with Baxter's exact solution, and weak universality is confirmed within the accuracy of the method due to the finite size of the system. In particular, the critical exponents η and δ are constant as required by weak universality. On the other hand, in the electric format, analytic formulas based on the scaling relations are derived for the critical exponents η_{e} and δ_{e} which agree with our numerical data. These exponents depend on the model's parameters which is evidence for the full nonuniversality of the symmetric eight-vertex model in the original electric formulation.
在正方形晶格上，对称（零电场）的 8 顶点模型的配分函数可以用原始的“电场”顶点格式或等效的“磁场”Ising 自旋格式来表示。在本文中，我们使用转角转移矩阵重整化群方法（该方法可提供可靠的数据）对模型的电场和磁场版本进行数值研究。重点放在通过两个标度关系相关的四个特定临界指数和中心电荷的计算上。该数值方法首先在磁场格式中进行了测试，得到的临界指数与 Baxter 的精确解一致，并且由于系统的有限大小，在该方法的精度范围内证实了弱普遍性。特别是，临界指数 η 和 δ 是弱普遍性所要求的常数。另一方面，在电场格式中，我们基于标度关系推导出了电场形式的临界指数 η_{e}和 δ_{e}的解析公式，这些公式与我们的数值数据一致。这些指数取决于模型的参数，这表明原始电场形式的对称 8 顶点模型具有完全的非普遍性。
