A Marginal Dimension of a Weakly Diluted Quenched m-Vector Model

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We calculate a marginal order parameter dimension mc which in a weakly diluted quenched m-vector model controls the crossover from a universality class of a ``pure'' model (m>mc) to a new universality class (m<mc). Exploiting the Harris criterion and the field-theoretical renormalization group approach allows us to obtain mc as a five-loop ε-expansion as well as a six-loop pseudo-ε expansion. In order to estimate the numerical value of mc we process the series by precisely adjusted Padé--Borel--Leroy resummation procedures. Our final result mc=1.912±0.004<2 stems from the longer and more reliable pseudo-ε expansion, suggesting that a weak quenched disorder does not change the values of xy-model critical exponents as it follows from the experiments on critical properties of He⁴ in porous media.