A check of a \(D=4\) field-theoretical calculation using the high-temperature expansion for Dyson’s hierarchical model. (English) Zbl 0947.81525
Summary: We calculate the high-temperature expansion of the two-point function up to order 800 in \(\beta\). We show that estimations of the critical exponent \(\gamma\) based on asymptotic analysis are not very accurate in the presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form (\(\beta_c -\beta)^{-\gamma} (ln (\beta_c -\beta)^p +r)\), we show that the errors are minimized for \(\gamma=0.9997\) and \(p=0.3351\), in very good agreement with field-theoretical calculations. We briefly discuss the related questions of triviality and hyperscaling.
MSC:
| 81T10 | Model quantum field theories |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
Keywords:
two-point functionReferences:
| [1] | Wilson, K., Phys. Rev. D, 3, 1818 (1971) |
| [2] | Baker, G., Phys. Rev. B, 15, 1552 (1977) |
| [3] | Gaunt, D.; Sykes, M.; McKenzie, S., J. Phys. A, 12, 871 (1979) |
| [4] | Meurice, Y.; Ordaz, G.; Rodgers, V. G.J., J. Stat. Phys., 77, 607 (1994) |
| [5] | Brézin, E.; Le Guillou, J. C.; Zinn-Justin, J., (Domb, C.; Green, M. S., Phase Transitions and Critical Phenomena, Vol. 6 (1976), Academic Press: Academic Press New York) |
| [6] | (Levy, M.; Le Guillou, J. C.; Zinn-Justin, J., Phase Transitions (1982), Plenum: Plenum New York), Cargese · Zbl 0282.00009 |
| [7] | Baker, G.; Kawashima, N., Phys. Rev. Lett., 75, 994 (1995) |
| [8] | Baker, G., Phys. Rev. B, 5, 2622 (1972) |
| [9] | Koch, H.; Wittwer, P., Comm. Math. Phys., 164, 627 (1994) · Zbl 0838.47051 |
| [10] | Collet, P.; Eckmann, J.-P.; Hirsbrunner, B., Phys. Lett. B, 71, 385 (1977) |
| [11] | Meurice, Y.; Ordaz, G., J. Stat. Phys., 82, 343 (1996) |
| [12] | Meurice, Y.; Ordaz, G., J. Phys. A, 29, L635 (1996) · Zbl 0900.82037 |
| [13] | Meurice, Y.; Ordaz, G.; Rodgers, V. G.J., Phys. Rev. Lett., 75, 4555 (1995) |
| [14] | Meurice, Y.; Niermann, S.; Ordaz, G., J. Stat. Phys., 87, 363 (1997) · Zbl 0925.82086 |
| [15] | Nickel, B., (Levy, M.; Le Guillou, J. C.; Zinn-Justin, J., Lecture Notes published in Phase Transitions (1982), Plenum: Plenum New York), Cargese |
| [16] | Niemeijer, Th.; van Leeuwen, J., (Domb, C.; Green, M. S., Phase Transitions and Critical Phenomena, Vol. 6 (1976), Academic Press: Academic Press New York) |
| [17] | J.J. Godina, Y. Meurice andS. Niermann, Univ. of Iowa preprint 97-2501, CERN 97-251, hep-lat 9709097.; J.J. Godina, Y. Meurice andS. Niermann, Univ. of Iowa preprint 97-2501, CERN 97-251, hep-lat 9709097. |
| [18] | Guttmann, A. J., (Domb, C.; Lebowitz, Phase Transitions and Critical Phenomena, Vol. 13 (1989), Academic Press: Academic Press New York) |
| [19] | Parisi, G., Statistical Field Theory, ((1988), Addison Wesley: Addison Wesley New York), 559 |
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