Perturbative vs. Non-Perturbative Study of the Sine-Gordon Model

Abstract

Functional Renormalization Group (FRG) flow equations of Sine-Gordon model in 1, 2 and 3 dimensions are obtained by using power law regulator in additive and multiplicative approaches in the leading order and next to leading order in the Taylor expansion of the Fourier amplitude with LPA′ and single Fourier mode approximations. The 2-dimensional FRG flow equations are compared to the Perturbative Renormalization Group (PRG) flow equations of Daniel J Amit, Yadin Y Goldschmidt, and S Grinstein. Renormalisation group analysis of the phase transition in the 2d coulomb gas, sine-gordon theory and xy-model. Journal of Physics A: Mathematical and General, 13(2):585, 1980., where a universal behaviour is claimed. This thesis explored whether FRG also reproduces this universal behaviour and it is concluded that no such universal behaviour exists in the FRG framework.