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Carlos I. Perez-Sanchez
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Recently, [JHEP 20 131 (2020)] obtained (a similar, scaled version of) the ($a,b$)-phase diagram derived from the Kazakov--Zinn-Justin solution of the Hermitian two-matrix model with interactions [mathrm{Tr,}Big{frac{a}{4} (A^4+B^4)+frac{b}{2} ABABBig},,] starting from Functional Renormalization. We comment on something unexpected: the phase diagram of [JHEP 20 131 (2020)] is based on a $beta_b$-function that does not have the one-loop structure of the Wetterich-Morris Equation. This raises the question of how to reproduce the phase diagram from a set of $beta$-functions that is, in its totality, consistent with Functional Renormalization. A non-minimalist, yet simple truncation that could lead to the phase diagram is provided. Additionally, we identify the ensemble for which the result of op. cit. would be entirely correct.
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