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Infrared properties of scalar field theories

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posted on 2023-06-08, 15:08 authored by Edouard Marchais
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 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.

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  • Published version

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141.0

Department affiliated with

  • Physics and Astronomy Theses

Qualification level

  • doctoral

Qualification name

  • phd

Language

  • eng

Institution

University of Sussex

Full text available

  • Yes

Legacy Posted Date

2013-06-28

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