单酉矩阵模型的相结构与非零β函数注记
Notes on phase structure and non-vanishing $β$ functions of one-unitary matrix model
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中文总结 AI 辅助
本文研究单酉矩阵模型，提出通过经典势形变确定相图定性结构的方法，证明临界线上的β函数非零，推广GWW情形并指出存在三阶相变。
中文摘要 AI 辅助
酉矩阵模型在诸多领域中发挥重要作用，尤其可用来表示不规则共形块，进而描述某些渐近自由超对称规范理论的低能有效作用量（LEEA）。本文提出一种通过经典势的形变确定相图定性结构的方法，并以包含最高到n≤3的cosnα项的实例进行说明。我们指出，临界“线”上的一组β函数处处为非零矢量，这一结论推广了n=1的GWW情形，且表明存在三阶（而非二阶）相变，与 susceptibility 指数的取值范围相符。
英文摘要
Unitary matrix models, among other things, play an important role in representing the irregular conformal block and hence LEEA of some asymptotically free susy gauge theories. Here, we develop a method of how to determine the qualitative structure of phase diagram by the deformation of classical potential, and illustrate this by the examples that contain term up to $\cos nα$, $n \leq 3$. We point out that a set of $β$ functions on critical ``lines" is nowhere a vanishing vector. This generalizes the $n =1$ GWW case and tells us the third order (rather than second order) phase transition in conformity with the range of values for the susceptibility exponent.
