Journal of Physical Studies 5(3/4), 261–267 (2001)
DOI: https://doi.org/10.30970/jps.05.261

A THREE-DIMENSIONAL RANDOM ISING MODEL: RESUMMATION OF FIVE-LOOP SERIES

V. Blavats'ka^{1}, Yu. Holovatch^{1,2}
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 investigate the critical behaviour of a $d=3$-dimensional weakly diluted quenched Ising model, analyzing the series for the renormalization group functions at $d=3$ obtained in a minimal subtraction scheme. Formerly it was established [R. Folk, Yu. Holovatch, T. Yavorskii, Phys. Rev. B {\bf 61}, 15 114 (2000)] that the resummed renormalization group series possess an ‟optimal truncation" behaviour, provided that a Chisholm-Borel resummation technique is applied. This resulted in a conjecture that a four-loop approximation is a final one for the random Ising model renormalization-group functions in a $d=3$ minimal subtraction scheme. We apply the method of subsequent resummation, developed in the context of the $d=0$-dimensional random Ising model, discuss the convergence properties of the series and give the results of the critical exponents increasing the order of approximation to 5-loop level.

PACS number(s): 05.10.Cc, 61.43.-j, 64.60.-i, 75.10.Hk