Five-loop \(\varepsilon\) expansion for \(O(n)\times O(m)\) spin models. (English) Zbl 1036.82506
Summary: We compute the renormalization group functions of a Landau-Ginzburg-Wilson Hamiltonian with \(O(n)\times O(m)\) symmetry up to five-loop in minimal subtraction scheme. The line \(n^+(m,d)\), which limits the region of second-order phase transition, is reconstructed in the framework of the \(\epsilon=4-d\) expansion for generic values of \(m\) up to \(O(\varepsilon^5)\). For the physically interesting case of noncollinear but planar orderings \((m=2)\) we obtain \(n^+(2,3)=6.1(6)\) by exploiting different resummation procedures. We substantiate this results reanalyzing six-loop fixed dimension series with pseudo-\(\epsilon\) expansion, obtaining \(n^+(2,3)=6.22(12)\). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for \(n>n^+\).
MSC:
82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
82B28 | Renormalization group methods in equilibrium statistical mechanics |
82B26 | Phase transitions (general) in equilibrium statistical mechanics |
82B27 | Critical phenomena in equilibrium statistical mechanics |
Keywords:
renormalization group functions; Landau-Ginzburg-Wilson Hamiltonian; second-order phase transition regionReferences:
[1] | Kawamura, H., J. Phys.: Condens. Matter, 10, 4707 (1998) |
[2] | Collins, M. F.; Petrenko, O. A., Can. J. Phys., 75, 605 (1997) |
[3] | Pelissetto, A.; Vicari, E., Phys. Rep., 368, 549 (2002) · Zbl 0997.82019 |
[4] | Delamotte, B.; Mouhanna, D.; Tissier, M. |
[5] | Bailin, D., J. Phys. C: Solid State Phys., 10, 1159 (1977) |
[6] | Kawamura, H., J. Phys. Soc. Jpn., 59, 2305 (1990) |
[7] | Kawamura, H., Phys. Rev. B, 42, 2610 (1990), Erratum |
[8] | Calabrese, P.; Pelissetto, A.; Vicari, E., Phys. Rev. B, 67, 054505 (2003) |
[9] | Calabrese, P.; Pelissetto, A.; Rossi, P.; Vicari, E. |
[10] | Pelissetto, A.; Rossi, P.; Vicari, E., Nucl. Phys. B, 607, 605 (2001) · Zbl 0969.82506 |
[11] | Gracey, J. A., Nucl. Phys. B, 644, 433 (2002) · Zbl 0999.82009 |
[12] | Parruccini, P., Phys. Rev. B, 68, 104415 (2003) |
[13] | Azaria, P.; Delamotte, B.; Delduc, F.; Jolicoeur, T., Nucl. Phys. B, 408, 485 (1993) · Zbl 1043.82535 |
[14] | Tissier, M.; Mouhanna, D.; Delamotte, B., Phys. Rev. B, 61, 15327 (2000) |
[15] | Antonenko, S. A.; Sokolov, A. I.; Varnashev, K. B., Phys. Lett. A, 208, 161 (1995) |
[16] | Antonenko, S. A.; Sokolov, A. I., Phys. Rev. B, 49, 15901 (1994) |
[17] | Loison, D.; Sokolov, A. I.; Delamotte, B.; Antonenko, S. A.; Schotte, K. D.; Diep, H. T., Pis’ma Zh. Eksp. Teor. Fiz.. Pis’ma Zh. Eksp. Teor. Fiz., JETP Lett., 72, 337 (2000) |
[18] | Pelissetto, A.; Rossi, P.; Vicari, E., Phys. Rev. B, 63, 140414 (2001) |
[19] | Calabrese, P.; Parruccini, P.; Sokolov, A. I., Phys. Rev. B, 66, 180403 (2002) |
[20] | Calabrese, P.; Parruccini, P.; Sokolov, A. I., Phys. Rev. B, 68, 094415 (2003) |
[21] | Ono, T., J. Magn. Magn. Matter, 177-181, 735 (1998) |
[22] | Loison, D.; Diep, H. T., Phys. Rev. B, 50, 16453 (1994) |
[23] | Itakura, M., J. Phys. Soc. Jpn., 72, 74 (2003) |
[24] | Loison, D.; Schotte, K. D., Eur. Phys. J. B, 14, 125 (2000) |
[25] | Tissier, M.; Delamotte, B.; Mouhanna, D., Phys. Rev. Lett., 84, 5208 (2000) |
[26] | Tissier, M.; Delamotte, B.; Mouhanna, D., Phys. Rev. B, 67, 134422 (2003) |
[27] | Tissier, M.; Delamotte, B.; Mouhanna, D., Int. J. Mod. Phys. A, 16, 2131 (2001) · Zbl 0980.81041 |
[28] | Pelissetto, A.; Rossi, P.; Vicari, E., Phys. Rev. B, 65, 020403 (2002) |
[29] | Le Guillou, J. C.; Zinn-Justin, J., Phys. Rev. B, 21, 3976 (1980), The pseudo-\(ϵ\) expansion was introduced by B.G. Nickel, see Ref. [19] in · Zbl 0978.82507 |
[30] | Folk, R.; Holovatch, Yu.; Yavors’kii, T., Phys. Rev. B, 62, 12195 (2000) |
[31] | Holovatch, Yu.; Dudka, M.; Yavors’kii, T., J. Phys. Studies, 5, 233 (2001) · Zbl 1081.82553 |
[32] | Zumbach, G., Nucl. Phys. B, 413, 771 (1994) |
[33] | Unpublished; Unpublished |
[34] | Calabrese, P.; Orlov, E. V.; Parruccini, P.; Sokolov, A. I., Phys. Rev. B, 67, 024413 (2003) |
[35] | Caffarel, M., Phys Rev. B, 64, 014412 (2001) |
[36] | Mailhot, A.; Plumer, M. L., Phys. Rev. B, 48, 9881 (1993) |
[37] | Kleinert, H.; Schulte-Frohlinde, V., Critical Properties of \(φ^4\)-Theories (2001), World Scientific: World Scientific Singapore · Zbl 1033.81007 |
[38] | Kleinert, H.; Neu, J.; Schulte-Frohlinde, V.; Chetyrkin, K. G.; Larin, S. A., Phys. Lett. B, 319, 545 (1993), Erratum |
[39] | Mudrov, A. I.; Varnashev, K. B., J. Phys. A, 34, L347 (2001) · Zbl 0984.80005 |
[40] | Kleinert, H.; Schulte-Frohlinde, V., Phys. Lett. B, 342, 284 (1995) |
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