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We calculate the critical exponent $\eta$ of the $D$-dimensional Ising model from a simple truncation of the functional renormalization group flow equations for a scalar field theory with long-range interaction.
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Note that in field-theoretical renormalization group calculations tadpole diagrams can be eliminated by performing an appropriate additive renormalization of the momentum independent part of the self energy, see e.g. D. J. Amit and V. Martin-Mayor, Field Theory, the Renormalization Group and Critical Phenomena
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