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arXiv 1902.07642hep-thcond-mat.stat-mech
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双曲sine-Gordon模型的重整化群分析--渐近无cosh相互作用--

Renormalization group analysis of the hyperbolic sine-Gordon model -- Asymptotic freedom from cosh interaction --

Takashi Yanagisawa

备注：
6 pages, 4 figures
发表信息：
Progress of Theoretical and Experimental Physics 2019, 023A01 (2019)
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摘要：

本文对二维双曲sine-Gordon模型进行了重整化群分析。我们基于维正则化方法和Wilson方法导出了重整化群方程。使用这两种方法得到相同的方程。我们有两个参数$α$和$β\equiv \sqrt{t}$，其中$α$表示真实萨拉场的相互作用强度，而$t=β^2$与动作的归一化有关。我们证明了$α$在高能区重整化为零，即sinh-Gordon理论是一个渐近自由理论.我们还证明了$t$的β函数在二维中为零的非重整化性质。

英文摘要：

We present a renormalization group analysis for the hyperbolic sine-Gordon (sinh-Gordon) model in two dimensions. We derive the renormalization group equations based on the dimensional regularization method and the Wilson method. The same equations are obtained using both these methods. We have two parameters $α$ and $β\equiv \sqrt{t}$ where $α$ indicates the strength of interaction of a real salar field and $t=β^2$ is related with the normalization of the action. We show that $α$ is renormalized to zero in the high-energy region, that is, the sinh-Gordon theory is an asymptotically free theory. We also show a non-renormalization property that the beta function of $t$ vanishes in two dimensions.

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