Abstract
This paper studies the number and the nature of the fixed points of the renormalization group for the ϕ4 model, as used for instance in the Landau theory of second order phase transitions. It is shown that when it exists the stable fixed point is unique and a condition on its symmetry is given: it is often larger than the initial symmetry. Finally counter examples, with v arbitrarily large, are given to the Dzyaloshinskii conjecture that there exist no stable fixed points when the Landau potential depends on more than v = 3 parameters.
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Michel, L. (1984). The Symmetry and Renormalization Group Fixed Points of Quartic Hamiltonians. In: Bars, I., Chodos, A., Tze, CH. (eds) Symmetries in Particle Physics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5313-1_6
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DOI: https://doi.org/10.1007/978-1-4899-5313-1_6
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