Original and modified non-perturbative renormalization group equations of the BMW scheme at the arbitrary order of truncation - Kaupužs, J.; Melnik, R. V. N. (Frontiers in Physics, 2024)
We consider the nonperturbative RG equations, obtained as approximations of the exact Wetterich RG flow equation within the Blaizot-Mendez-Wschebor (BMW) truncation scheme. For the first time, we derive explicit RG flow equations for the scalar model at arbitrary order of truncation. Moreover, we consider original, as well as modified approximations, used to obtain a set of closed equations. We compare these equations at the s = 2 order of truncation with those recently derived in J. Phys. A: Math. Theor. 53, 415002 (2020) within a new truncation scheme and find a striking similarity. Namely, the first-order equations of the latter scheme, those of the original BMW scheme and those of the modified here BMW scheme (at s = 2) differ only in one term. We have solved these equations by a recently proposed and tested method of semi-analytic approximations. Thus, the critical exponents η, ν and ω have been evaluated, recovering also the known results of the original BMW scheme. In addition, we have estimated the subleading correction-to-scaling exponent ω 2 for the three equations considered. To the best of our knowledge, this exponent has not been yet extracted from the Wetterich equation beyond the local potential (the zeroth order) approximation. Our current estimate for the 3D Ising model is ω 2 = 2.02(40), where the error bars include the expected truncation error in the BMW scheme.