Sine-Gordon revisited

We study the sine-Gordon model in two dimensional space time in two differe nt domains. For beta > 8 pi and weak coupling, we introduce an ultraviolet cutoff and study the infrared behavior. A renormalization group analysis sh ows that the model is asymptotically free in the infrared. For beta < 8 pi and weak coupling, we introduce an infrared cutoff and study the ultraviole t behavior. A renormalization group analysis shows that the model is asympt otically free in the ultraviolet.