Prog. Theor. Phys. Vol. 64 No. 3 (1980) pp. 813-819
Modification of 1/n Expansion in Critical Phenomena
Department of Pure and Applied Sciences, University of Tokyo, Komaba, Tokyo 153
(Received April 14, 1980)
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.
DOI : 10.1143/PTP.64.813
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