Geodesic
The $1/N$ expansion in the $O(N)\times O(N)$ scalar theory and the problem of the restoration of symmetry at high temperatures
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 363-371 
K. G. Klimenko. The $1/N$ expansion in the $O(N)\times O(N)$ scalar theory and the problem of the restoration of symmetry at high temperatures. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 363-371. http://geodesic.mathdoc.fr/item/TMF_1989_80_3_a3/
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     author = {K. G. Klimenko},
     title = {The $1/N$ expansion in~the $O(N)\times O(N)$ scalar theory and the problem of~the restoration of~symmetry at~high temperatures},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {1989},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of symmetry restoration at high temperatures in the model (1) is considered. The large $N$ expansion method in space-time dimensions $d=3,4$ is used. In the case $d=4$ and $T=0$ the initial symmetry remains intact and the problem stays open. In the case $d=3$ the symmetry may be broken spontaneously at $T=0$ but it is always restored at $T\to\infty$.

[1] Kirzhnitz D. A., Linde A., Phys. Lett., B42:4 (1972), 471–474 | DOI

[2] Weinberg S., Phys. Rev., D9:12 (1974), 3357–3378

[3] Mohapatra R. N., Senjanović G., Phys. Rev., D20:12 (1979), 3390–3398

[4] Salomonson P., Skagerstam B.-S. K., Stern A., Phys. Lett., 151B:3–4 (1985), 243–246 | DOI

[5] Fujimoto Y., Sakakibara S., Phys. Lett., B151:3–4 (1985), 260–262 | DOI

[6] Fujimoto Y., Wipf A., Yoneyama H., Z. Phys., C35:3 (1987), 351–354

[7] Kobayashi M., Kugo T., Prog. Theor. Phys., 54:5 (1975), 1537–1545 ; Graziany F. R., Ann. Phys., 151:2 (1983), 265–310 | DOI | DOI

[8] Klimenko K. G., Leading order of $1/N$ expansion in $O(N)\times O(N)$ scalar field theory, Preprint IHEP 87-166, IHEP, Serpukhov, 1987 | MR

[9] Klimenko K. G., TMF, 62:1 (1985), 87–96 | MR

[10] Dolan L., Jackiw R., Phys. Rev., D9:12 (1974), 3320–3341 | MR

[11] Haber H. E., Weldon H. A., J. Math. Phys., 23:10 (1982), 1852–1858 | DOI | MR

[12] Klimenko K. G., Gaussian effective potential and symmetry restoration at high temperatures in four-deminsional $O(N)\times O(N)$ field theory, Preprint IHEP 88-84, IHEP, Serpukhov, 1988 | MR