Journal of Physical Studies 5(3/4), 233–239 (2001) DOI: https://doi.org/10.30970/jps.05.233 A MARGINAL DIMENSION OF A WEAKLY DILUTED QUENCHED m-VECTOR MODEL Yu. Holovatch{1,2}, M. Dudka1, T. Yavors'kii2 1Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine 1 Svientsitskii Str., Lviv, UA–79011, Ukraine 2Ivan Franko National University of Lviv, Department for Theoretical Physics 12 Drahomanov Str., Lviv, UA–79005, Ukraine

We calculate a marginal order parameter dimension $m_c$ which in a weakly diluted quenched $m$-vector model controls the crossover from a universality class of a ‟pure” model ($m>m_c$) to a new universality class ($m<m_c$). Exploiting the Harris criterion and the field-theoretical renormalization group approach allows us to obtain $m_c$ as a five-loop $ε$-expansion as well as a six-loop pseudo-$ε$ expansion. In order to estimate the numerical value of $m_c$ we process the series by precisely adjusted Padé-Borel-Leroy resummation procedures. Our final result $m_c=1.912\pm0.004<2$ 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 ${\rm He}^4$ in porous media.

PACS number(s): 05.50.+q, 64.60.Ak, 75.10.Hk

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