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## Infrared properties of scalar field theories

### Abstract

Phase transitions and critical phenomena are of central importance in quantum field theory and statistical physics. We investigate the low energy properties of O(N) symmetric\ud scalar field theories using functional renormalisation group methods for all N. This modern formulation of Wilson's renormalisation group allows a continuous interpolation between short and long distance physics without resorting to a weak coupling expansion. To leading order in the derivative expansion, we study the phase transition and the approach to convexity in the deep infrared limit. In the limit of infinite N, the fluctuations of the Goldstone modes dominate allowing for a complete analytical discussion of the effective potential. For finite N, the radial fluctuations become important and we resort to systematic series expansions. In both cases a systematic and thorough analysis of the diverse fixed point solutions is carried out. This leads to a comprehensive picture of the scaling potential for a large number of universality classes. We also study the dependence of our results on the regularisation scheme. Finally, we establish that the infrared completion of the effective potential in the broken phase is driven by a fixed point that leads to the flattening of the non-convex part of the potential

Topics: QC0770
Year: 2013
OAI identifier: oai:sro.sussex.ac.uk:45244

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