Geodesic
Goldstone singularities in the $4-\varepsilon$ expansion of the $\Phi^4$ theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 2, pp. 212-225

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A scheme of resummation of singularities related to the Goldstone singularities is suggested for the series of $4-\varepsilon$ expansions of the Green functions of the $n$-component $\Phi^4$ theory below the critical temperature. Using this scheme it is proved (in the arbitrary order of the $\varepsilon$ expansion) that the scaling functions in the neighbourhood of the critical point have the same asymptotics at small external field and momenta as those predicted by the “hydrodynamic approximation”. 
@article{TMF_1989_80_2_a3,
     author = {M. Yu. Nalimov},
     title = {Goldstone singularities in the $4-\varepsilon$ expansion of the $\Phi^4$ theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {212--225},
     publisher = {mathdoc},
     volume = {80},
     number = {2},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a3/}
}
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M. Yu. Nalimov. Goldstone singularities in the $4-\varepsilon$ expansion of the $\Phi^4$ theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 2, pp. 212-225. http://geodesic.mathdoc.fr/item/TMF_1989_80_2_a3/