Borel resummation of the~$\varepsilon$-expansion of the~dynamical exponent $z$ in model~A of the~$\phi^4(O(n))$ theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 1, pp. 96-108
Voir la notice de l'article provenant de la source Math-Net.Ru
We perform the Borel resummation of the currently known terms of the $\varepsilon$-expansion up to order $\varepsilon^4$ of the dynamical exponent $z$ in the critical-behavior model A. We obtain the large-order asymptotic approximation of the $\varepsilon$-expansion of the dynamical exponent and find a significant discrepancy between the currently calculated orders of the expansion and the obtained asymptotic values. We discuss the influence of this deviation on the accuracy of the resummation results.
Keywords:
Borel resummation, dynamical exponent, critical behavior, large-order asymptotic approximation.
@article{TMF_2009_159_1_a5,
author = {M. Yu. Nalimov and V. A. Sergeev and L. Sladkoff},
title = {Borel resummation of the~$\varepsilon$-expansion of the~dynamical exponent $z$ in {model~A} of the~$\phi^4(O(n))$ theory},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {96--108},
publisher = {mathdoc},
volume = {159},
number = {1},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2009_159_1_a5/}
}
TY - JOUR AU - M. Yu. Nalimov AU - V. A. Sergeev AU - L. Sladkoff TI - Borel resummation of the~$\varepsilon$-expansion of the~dynamical exponent $z$ in model~A of the~$\phi^4(O(n))$ theory JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2009 SP - 96 EP - 108 VL - 159 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2009_159_1_a5/ LA - ru ID - TMF_2009_159_1_a5 ER -
%0 Journal Article %A M. Yu. Nalimov %A V. A. Sergeev %A L. Sladkoff %T Borel resummation of the~$\varepsilon$-expansion of the~dynamical exponent $z$ in model~A of the~$\phi^4(O(n))$ theory %J Teoretičeskaâ i matematičeskaâ fizika %D 2009 %P 96-108 %V 159 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2009_159_1_a5/ %G ru %F TMF_2009_159_1_a5
M. Yu. Nalimov; V. A. Sergeev; L. Sladkoff. Borel resummation of the~$\varepsilon$-expansion of the~dynamical exponent $z$ in model~A of the~$\phi^4(O(n))$ theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 1, pp. 96-108. http://geodesic.mathdoc.fr/item/TMF_2009_159_1_a5/