On the massive sine-Gordon equation in all regions of collapse
The paper deals with the two dimensional sine-Gordon model which presents interest in quantum field theory as well as in statistical mechanics, where the potential \[ (1)\quad V_ 0[\Lambda]:=\lambda \int_{\Lambda} : \cos \alpha \phi_{\xi} : d\xi \quad \Lambda \subset {\mathbb{R}}^ 2 \] refers to a two dimensional gas of spinless particles with Yukawa interaction in the grand canonical ensemble. In (1) \(\lambda\) is the activity and the inverse temperature of the gas is such that \(\alpha^ 2=\beta e^ 2\), where \(\pm e\) are the charges of the particles. According to previous papers, the gas is stable for \(\beta e^ 2<4\pi\), while at \(\beta e^ 2=8\pi\) one expects full collapse. The ultraviolet stability for all values \(\alpha^ 2\in [4\pi,8\pi[\) is established by means of renormalization group techniques.
scientific article; zbMATH DE number 4036330