Degeneracy induced scaling of the correlation length for periodic models

Abstract

The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz-Thouless type phase transition.

Truncation effects in the functional renormalization group study of spontaneous symmetry breaking

“…In d = 4, the WF fixed point (green dot in figure 1) merges to the Gaussian one (black). The IR fixed point (red) appears in any dimensions and is related to the convexity of the potential [47][48][49][50][51][52].…”

Critical exponents in quantum Einstein gravity

“…This is the case in QEG, too [21][22][23]. We calculated the exponent ν by the dynamically induced correlation [23,32,33] around the IR fixed point. We obtained that the exponent ν around the IR fixed point equals the one calculated around the GFP and it is ν = 1/2.…”

Asymptotic safety in the sine-Gordon model

“…In the IR limit, the MSG model shows a second order phase transition. There, we got ν ¼ 1=2 [30] for the exponent of the correlation length in Eq. (13).…”

“…It was shown that there exists an IR fixed point [23,24], which appears in the low energy-scaling regime of the broken symmetric phase. There are further models where the IR fixed point was identified successfully [24,[26][27][28][29][30][31].…”

“…In the UV limit, the mass dies out; therefore, the model shows an essential scaling. However, in the IR, where the mass becomes more and more important, the essential scaling is replaced by a scaling belonging to a second order phase transition [30].…”