Abstract
The principles of the recent calculations of critical exponents from three- and two-dimensional field theory are reviewed. They rely on the Callan-Symanzik equations, diagram calculations, and on the characterization of the asymptotic behavior of perturbation series at large order. We then present new results concerning the normalization of the large-order behavior.
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G. A. Baker, B. G. Nickel, M. S. Green, and P. I. Meiron,Phys. Rev. Lett. 36:1351 (1976); J. C. Le Guillou and J. Zinn-Justin,Phys. Rev. Lett. 39:95 (1977); G. A. Baker, B. S. Nickel, and P. I. Meiron, Saclay Preprint 77-39.
C. S. Lam,Nuovo Cimento 55:258 (1968); L. U. Lipatov,Zh. Eksp. Teor. Fiz. 72:411 (1977); E. Brézin, J. C. Le Guillou, and J. Zinn-Justin,Phys. Rev. D 15:1544 (1977).
K. Wilson and J. Kogut,Phys. Rep.12C:75 (1974); K. Wilson,Rev. Mod. Phys. 47:773 (1975); inPhase Transitions and Critical Phenomena, Vol. VI, C. Domb and M. S. Green, eds. (Academic, New York, 1976); S. K. Ma,Modern Theory of Critical Phenomena (Benjamin, Reading, Mass., 1976).
E. Brézin, J. C. deLe Guillou, and J. Zinn-Justin, inPhase Transitions and Critical Phenomena, Vol. VI, C. Domb and M. S. Green, eds. (Academic, New York, 1976); see also C. Di Castro,Nuovo Cimento Lett. 5:69 (1972); K. Symanzik (unpublished), as quoted in G. Mack,Lecture Notes in Physics, Vol. 17 (Springer Verlag, Berlin, 1973); P. K. Mitter,Phys. Rev. D 7:2927 (1973); B. Schroer,Phys. Rev. B 8:4200 (1973).
J. Glimm and A. Jaffe,Notes of the 1976 Cargèse Summer School.
K. Symanzik,Comm. Math. Phys. 18:227 (1970); J. Callan,Phys. Rev. D 1:1541 (1971).
G. Parisi,Notes of the 1973 Cargèse Summer School.
B. G. Nickel, Critical Exponents via theε expansion: A Study of Terms beyondε 3, Oxford Preprint (1974), unpublished.
B. G. Nickel, D. I. Meiron, and G. A. Baker, Compilation of 2-pt and 4-pt Graphs, University of Guelph Report (1977); Evaluation of Series for Critical Exponents for aφ model in 3 and 2 Dimensions,Phys. Rev., to be published.
B. G. Nickel,J. Math. Phys. 19:542 (1978).
F. J. Dyson,Phys. Rev. 85:631 (1952); J. S. Langer,Ann. Phys. (N. Y.) 41:108 (1967).
T. Banks, C. M. Bender, and T. T. Wu,Phys. Rev. D 8:3346 (1973).
G. Parisi,Phys. Lett. 67B:167 (1977); C. Itzykson, G. Parisi, and J. B. Zuber,Phys. Rev. Lett. 38:306 (1977); J. R. Klauder,Acta Phys. Austriaca Suppl. 11:341 (1973); E. M. Stein,Singular Integrals and Differentiability Properties of Functions (Princeton Univ. Press, Princeton, N.J., 1970); S. Coleman, V. Glaser, and A. Martin,Comm. Math. Phys. 58:211 (1978).
E. Brézin, J. C. Le Guillou, and J. Zinn-Justin,Phys. Rep. D 15:1558 (1977).
S. Graffi, V. Grecchi, and B. Simon,Phys. Lett. 32B:631 (1970); J. D. Eckmann, J. Magnen, and R. Sénéor,Comm. Math. Phys. 39:251 (1975).
J. Zittartz and J. S. Langer,Phys. Rev. 148:741 (1966); J. L. Gervais and B. Sakita,Phys. Rev. D 11:2943 (1975); V. E. Korepin, P. P. Kulish, and L. D. Faddeev,JETP Lett. 21:138 (1975).
C. Itzykson, G. Parisi, and J. B. Zuber,Phys. Rev. D 16, 996 (1977).
V. Glaser, H. Grosse, A. Martin, and W. Thirring, inStudies in Mathematical Physics, Essays in Honor of V. Bargman, E. Liebet al., eds. (Princeton Univ. Press, Princeton, N.J., 1976).
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On leave of absence from INFN, Frascati.
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Brézin, E., Parisi, G. Critical exponents and large-order behavior of perturbation theory. J Stat Phys 19, 269–292 (1978). https://doi.org/10.1007/BF01011726
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DOI: https://doi.org/10.1007/BF01011726