Convergence of derivative expansions of the renormalization group

Journal of High Energy Physics

Volumn 3, Issue 8, 1999, Pages

  Morris, Tim R ^a   Tighe, John F ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Non perturbative Effects; Renormalization Regularization and Renormalons

Indexed keywords

EID: 33645917702     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/1999/08/007     Document Type: Article

References (49)

1. T.R. Morris, The exact renormalization group and approximate solutions, Int. J. Mod. Phys. A 9 (1994) 2411 [hep-ph/9308265].
2. T.R. Morris, Elements of the continuous renormalization group, Prog. Theor. Phys. Suppl. 131 (1998) 395 [hep-th/9802039].
3. J.F. Nicoll, T.S. Chang and H.E. Stanley, Approximate renormalization group based on the Wegner-Houghton differential generator, Phys. Rev. Lett. 33 (1974) 540.
4. F.J. Wegner and A. Houghton, Renormalization group equation for critical phenomena, Phys. Rev. A 8 (1973) 401;
5. M. D'Attanasio and T.R. Morris, Large-N and the renormalization group, Phys. Lett. B 409 (1997) 363 [hep-th/9704094].
6. S.-K. Ma, Introduction to the renormalization group, Rev. Mod. Phys. 45 (1973) 589;
7. T.S. Chang, D.D. Vvedensky and J.F. Nicoll, Differential renormalization-group generators for static and dynamical phenomena, Phys. Rev. 217 (1992) 279;
8. K.-I. Aoki et al., The effectiveness of the local potential approximation in the WegnerHoughton renormalization group Prog. Theor. Phys. 95 (1996) 409 [hep-ph/9612458].
9. 4 theory, Nucl. Phys. B 401 (1993) 567 [hep-ph/9301271].
10. T.R. Morris and M. Turner, Derivative expansion of the renormalization group in O(N) scalar field theory, Nucl. Phys. B 509 (1998) 637 [hep-th/9704202].
11. T.R. Morris, Derivative expansion of the exact renormalization group, Phys. Lett. B 329 (1994) 241 [hep-ph/9403340].
12. T.R. Morris, Three-dimensional massive scalar field theory and the derivative expansion of the renormalization group, Nucl. Phys. B 495 (1997) 477 [hep-th/9612117].
13. T.R. Morris, Properties of derivative expansion approximations to the renormalization group Int. J. Mod. Phys. B 12 (1998) 1343 [hep-th/9610012].
14. T.R. Morris, Momentum scale expansion of sharp cutoff flow equations, Nucl. Phys. B 458 (1996) 477 [hep-th/9508017].
15. T.R. Morris, in New developments in the continuous renormalization group in New Developments in Quantum Field Theory, NATO ASI series B, 366, Plenum Press 1998, hep-th/9709100.
16. J.R. Shepard, V. Dmitrasinovic and J.A. McNeil, Monte Carlo and renormalization group effective potentials in scalar field theories, Phys. Rev. D 51 (1995) 7017;
17. J.D. Shafer and J.R. Shepard, Monte carlo and renormalization group local effective potentials in scalar field theories at finite temperature, Phys. Rev. D 55 (1997) 4990.
18. R.D. Ball, P.E. Haagensen, J.I. Latorre, and E. Moreno, Scheme independence and the exact renormalization group Phys. Lett. B 347 (1995) 80 [hep-th/9411122].
19. G.R. Golner, Nonperturbative renormalization-group calculations for continuum spin systems, Phys. Rev. B 33 (1986) 7863;
20. J. Commellas, Polchinski equation, reparameterization invariance and the derivative expansion, Nucl. Phys. B 509 (1998) 662 [hep-th/9705129].
21. G. Zumbach, The re-normalization group in the local potential approximation and its applications to the O(N) model, Nucl. Phys. B 413 (1994) 754;
22. The local potential approximation of the renormalization group and its applications Phys. Lett. A 190 (1994) 225;
23. K.-I. Aoki et al., The effectiveness of the local potential approximation in the wegnerhoughton renormalization group, Prog. Theor. Phys. 95 (1996) 409 [hep-ph/9612458];
24. J. Comellas and A. Travesset, O(N) models within the local potential approximation, Nucl. Phys. B 498 (1997) 539 [hep-th/9701028];
25. R. Neves, Y. Kubyshin and R. Potting, Polchinski ERG equation and 2d scalar field theory, hep-th/9811151.
26. Y. Kubyshin, Exact renormalization group approach in scalar and fermionic theories, Int. J. Mod. Phys. B 12 (1998) 1321 [hep-th/9702082].
27. T.R. Morris, The renormalization group and two-dimensional multicritical effective scalar field theory, Phys. Lett. B 345 (1995) 139 [hep-th/9410141].
28. J.F. Nicoll and T.S. Chang, An exact one particle irreducible renormalization group generator for critical phenomena, Phys. Lett. A 62 (1977) 287;
29. M. Bonini et al., Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114].
30. C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90.
31. C. Wetterich, private communication.
32. N. Tetradis and C. Wetterich, Critical exponents from effective average action, Nucl. Phys. B 422 (1994) 541 [hep-ph/9308214];
33. 4 theories, Nucl. Phys. B 398 (1993) 659;
34. J. Berges, N. Tetradis and C. Wetterich, Coarse graining and first order phase transitions Phys. Lett. B 393 (1997) 387 [hep-ph/9610354];
35. Critical equation of state from the average action Phys. Rev. Lett. 77 (1996) 873 [hep-th/9507159];
36. D.U. Jungnickel and C. Wetterich, Flow equations for phase transitions in statistical physics and QCD hep-ph/9902316;
37. S. Seide and C. Wetterich, Equation of state near the endpoint of the critical line cond-mat/9806372;
38. J. Berges and C. Wetterich, Equation of state and coarse grained free energy for matrix models, Nucl. Phys. B 487 (1997) 675 [hep-th/9609019];
39. S. Bornholdt et al., Flow of the coarse grained free energy for crossover phenomena, Int. J. Mod. Phys. A 14 (1999) 899 [cond-mat/9603129];
40. High temperature phase transition in two scalar theories Phys. Rev. D 53 (1996) 4552 [hep-ph/9503282];
41. Coleman- Weinberg phase transition in two scalar models Phys. Lett. B 348 (1995) 89 [hep-th/9408132];
42. M. Grater and C. Wetterich, Kosterlitz-Thouless phase transition in the two dimensional linear sigma model, Phys. Rev. Lett. 75 (1995) 378 [hep-ph/9409459];
43. T. Papenbrock and C. Wetterich, Two loop results from one loop computations and non perturbative solutions of exact evolution equations, Z. Physik C 65 (1995) 519 [hep-th/9403164];
44. D. Litim et al., Nonperturbative analysis of the Coleman-Weinberg phase transition, Mod. Phys. Lett. A 12 (1997) 2287 [hep-ph/9407267];
45. N. Tetradis, Comparison of renormalization group and lattice studies of the electroweak phase transition, Phys. Lett. B 409 (1997) 355 [hep-ph/9611461].
46. M. Bonini et al., Beta function and infrared renormalons in the exact Wilson renormalization group in Yang-Mills theory, Nucl. Phys. B 483 (1997) 475 [hep-th/9604114].
47. K. Wilson and J. Kogut, The renormalization group and the epsilon expansion, Phys. Rep. 12 (1974) 75.
48. J. Polchinski, Renormalization and effective lagrangians Nucl. Phys. B 231 (1984) 269.
49. e.g., J. Zinn-Justin Quantum field theory and critical phenomena C.P., Oxford 1993.