We investigate some issues concerning the zero-momentum four-point renormalized coupling constant g in the symmetric phase of O(N) models, and the corresponding Callan-Symanzik beta-function. In the framework of the 1/N expansion we show that the Callan-Symanzik beta-function is non-analytic at its zero, i.e. at the fixed-point value g* of g. This fact calls for a check of the actual accuracy of the determination of g* from the resummation of the d = 3 perturbative g-expansion, which is usually performed assuming the analyticity of the beta-function. Two alternative approaches are exploited. We extend the epsilon-expansion of g* to O(epsilon(4)). Quite accurate estimates of g* are obtained by an analysis that exploits the analytic behavior of g* as a function of d and the known values of g* for lower-dimensional O(N) models, i.e. for d = 2, 1,0. Accurate estimates of g* are also obtained by a reanalysis of the strong-coupling expansion of the lattice N-vector model allowing for the leading confluent singularity. The agreement among the g-, epsilon-, and strong-coupling expansion results is good for all values of N. However, at N = 0, 1, epsilon- and strong-coupling expansion favor values of g* which are slightly lower than those obtained by the resummation of the g-expansion assuming the analyticity of the Callan-Symanzik beta-function. (C) 1998 Elsevier Science B.V.
Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
VICARI, ETTORE
1998-01-01
Abstract
We investigate some issues concerning the zero-momentum four-point renormalized coupling constant g in the symmetric phase of O(N) models, and the corresponding Callan-Symanzik beta-function. In the framework of the 1/N expansion we show that the Callan-Symanzik beta-function is non-analytic at its zero, i.e. at the fixed-point value g* of g. This fact calls for a check of the actual accuracy of the determination of g* from the resummation of the d = 3 perturbative g-expansion, which is usually performed assuming the analyticity of the beta-function. Two alternative approaches are exploited. We extend the epsilon-expansion of g* to O(epsilon(4)). Quite accurate estimates of g* are obtained by an analysis that exploits the analytic behavior of g* as a function of d and the known values of g* for lower-dimensional O(N) models, i.e. for d = 2, 1,0. Accurate estimates of g* are also obtained by a reanalysis of the strong-coupling expansion of the lattice N-vector model allowing for the leading confluent singularity. The agreement among the g-, epsilon-, and strong-coupling expansion results is good for all values of N. However, at N = 0, 1, epsilon- and strong-coupling expansion favor values of g* which are slightly lower than those obtained by the resummation of the g-expansion assuming the analyticity of the Callan-Symanzik beta-function. (C) 1998 Elsevier Science B.V.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
