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X is similar to the one encountered in hot three-dimensional quantum electrodynamic plasmas. There, the photons play the role of fluctuations at their critical point. The divergences are logarithmic in frequency. Furthermore, since the photons can be taken into account order by order in a systematic manner, an infinite resummation is possible. In our case, the spin propagator is not really a different physical entity and, as we saw, it is not clear how to implement a systematic diagrammatic approach. For more details,
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We thank D. Sénéchal and S. Pairault for discussion on this point.
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Once the expression for the self-energy has been written in the form equation (68), it can be interpreted as the leading self-energy of an electron interacting with a bosonic excitation. Numerous studies of this kind of problem have appeared, including some where the bosonic excitation is softening. For a recent example, see Crisan M. and Tataru L., J. Superconductivity 8 (1995) 341;
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