Quick Search:
Prog. Theor. Phys. Vol. 64 No. 3 (1980) pp. 813-819
Modification of 1/n Expansion in Critical Phenomena
Ryuzo Abe
Department of Pure and Applied Sciences, University of Tokyo, Komaba, Tokyo 153
(Received April 14, 1980)
Abstract:
If a function g(n) behaves as g(n) →n in the limit n →∞, formulas in 1/n expansion are formally converted into expansions in powers of 1/g(n). A criterion for the possibility of this modification is discussed, being referred to the existence of saddle points. It is shown that an expansion parameter 1/(n+m) or 2/ [ (n+m)+√(n+m)2-4B ] is allowed, whereas (n+C)/(n2+An+B) is not allowed in general. As an application, an interpolation formula which is exact at n=-2 and yields 1/n2 terms in the limit n →∞ is derived in the three-dimensional case. The result for r thus obtained leads to a fairly good agreement with numerical values, as compared to the original 1/n expansion.
URL :
http://ptp.ipap.jp/link?PTP/64/813/
DOI : 10.1143/PTP.64.813
References:
- R. Abe, Prog. Theor. Phys. 49 (1973), 113[PTP].
- R. Abe and S. Hikami, Prog. Theor. Phys. 49 (1973), 442[PTP].
- M. Suzuki, Renormalization Group in Critical Phenomena and Quantum Field Theory: Proceedings of a Conference, edited by J. D. Gunton and M. S. Green (Department of Physics, Temple University, Philadelphia, 1973), p. 55.
- Y. Okabe, (1979), unpublished.
-
K. G. Wilson and J. B. Kogut, Phys Rep. C 12 (1974), 75[CrossRef].
- R. Abe, Prog. Theor. Phys. 49 (1973), 1877[PTP].
- Y. Okabe and M. Oku, Prog. Theor. Phys. 60 (1978), 1277[PTP]; ibid. 60 (1978), 1287[PTP].
-
I. Kondor and T. Temesvári, Phys. Rev. B 21 (1980), 260[APS].
-
R. Balian and G. Toulouse, Phys. Rev. Lett. 30 (1973), 544[APS].
-
M. E. Fisher, Phys. Rev. Lett. 30 (1973), 679[APS].
-
R. Abe and A. Hatano, Phys. Lett. A 48 (1974), 281[CrossRef].
