标题： 热力学Bethe假设和格点模型与场论的有限尺寸修正的统一方法 显示英文标题

标题： Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories

摘要： 我们提出了一种统一的方法，用于磁链和场论的热力学Bethe假设(TBA)，该方法包括格点BA模型的有限尺寸（零温度）计算。 在所有情况下，自由能通过求解一个{\bf 单一}非线性积分方程(NLIE)来获得。 [嵌套BA中出现一组NLIE]。 我们推导了以下情况的NLIE：a) 具有扭曲边界条件的六顶点模型；b) 外部磁场中的XXZ链$h_z$；c) 周期性箱体大小为$\b \equiv 1/T $的sine-Gordon-质量Thirring模型(sG-mT)，使用光锥方法。 此NLIE在一种情况下通过迭代求解（XXZ链中的高$T$和sG-mT模型中的低$T$）。 在相反（共形）区域中，得到了主导行为的显式形式。 更高修正可以通过我们提出的NLIE的黎曼-希尔伯特形式得到。 显示英文摘要

摘要： We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for magnetic chains and field theories that includes the finite size (and zero temperature) calculations for lattice BA models. In all cases, the free energy follows by quadratures from the solution of a {\bf single} non-linear integral equation (NLIE). [A system of NLIE appears for nested BA]. We derive the NLIE for: a) the six-vertex model with twisted boundary conditions; b) the XXZ chain in an external magnetic field $h_z$ and c) the sine-Gordon-massive Thirring model (sG-mT) in a periodic box of size $\b \equiv 1/T $ using the light-cone approach. This NLIE is solved by iteration in one regime (high $T$ in the XXZ chain and low $T$ in the sG-mT model). In the opposite (conformal) regime, the leading behaviors are obtained in closed form. Higher corrections can be derived from the Riemann-Hilbert form of the NLIE that we present.