Abstract
We prove analyticity theorems in the coupling constant for the Hubbard model at half-filling. The model in a single renormalization group slice of index i is proved to be analytic in λ for |λ|≤c/i for some constant c, and the skeleton part of the model at temperature T (the sum of all graphs without two point insertions) is proved to be analytic in λ for |λ|≤c/|log T|2. These theorems are necessary steps towards proving that the Hubbard model at half-filling is not a Fermi liquid (in the mathematically precise sense of Salmhofer).
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Rivasseau, V. The Two Dimensional Hubbard Model at Half-Filling. I. Convergent Contributions. Journal of Statistical Physics 106, 693–722 (2002). https://doi.org/10.1023/A:1013770608643
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DOI: https://doi.org/10.1023/A:1013770608643