论文标题
扭曲的$ a_1^{（1）} $，$ a_2^{（1）} $和$ a_2^{（2）} $模型
Groundstate finite-size corrections and dilogarithm identities for the twisted $A_1^{(1)}$, $A_2^{(1)}$ and $A_2^{(2)}$ models
论文作者
论文摘要
我们考虑$ y $ - 系统由$ a_1^{（1）} $，$ a_2^{（1）} $，$ a_2^{（2）} $ dertex和Loop Models and Loop Models and loop Models and andity of Unity，cylinder上有扭曲的边界条件。顶点模型分别是6-，15-和Izergin-Korepin 19-Vertex模型。相应的循环模型分别是密集，完全填充和稀释的templeley-lieb循环模型。对于所有三个模型，我们的重点是与$ e^{iλ} $的统一值与交叉参数$λ$相对于这些模型的主要和双重系列。将已知的功能方程式转换为热力学Bethe Ansatz（TBA）方程的形式的非线性积分方程，我们将$ Y $ - 系统求解了有限大小的$ \ frac 1n $校正，以遵循Klümper和Pearce的方法。 $ C-24δ$的结果表达式（其中$ c $是中央电荷，$δ$是与地面施工相关的共形重量，是使用各种Diologarithm身份简化的。我们的分析结果与以前通过不同方法获得的结果一致，并且对于$ a_2^{（1）} $模型的双重系列是新的。
We consider the $Y$-systems satisfied by the $A_1^{(1)}$, $A_2^{(1)}$, $A_2^{(2)}$ vertex and loop models at roots of unity with twisted boundary conditions on the cylinder. The vertex models are the 6-, 15- and Izergin-Korepin 19-vertex models respectively. The corresponding loop models are the dense, fully packed and dilute Temperley-Lieb loop models respectively. For all three models, our focus is on roots of unity values of $e^{iλ}$ with the crossing parameter $λ$ corresponding to the principal and dual series of these models. Converting the known functional equations to nonlinear integral equations in the form of Thermodynamic Bethe Ansatz (TBA) equations, we solve the $Y$-systems for the finite-size $\frac 1N$ corrections to the groundstate eigenvalue following the methods of Klümper and Pearce. The resulting expressions for $c-24Δ$, where $c$ is the central charge and $Δ$ is the conformal weight associated with the groundstate, are simplified using various dilogarithm identities. Our analytic results are in agreement with previous results obtained by different methods and are new for the dual series of the $A_2^{(1)}$ model.
