Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models

Details Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models

1997-11-10

arxiv.org/abs/cond-mat/9711078v2

Nucl.Phys. B519 (1998) 626-660

Physics

Condensed Matter

35 pages (3 figs), added Ref. for GRT, some estimates are revised, other minor changes

Scientific paper

10.1016/S0550-3213(98)00164-3

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 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 then obtained by an analysis exploiting the analytic behavior of g^* as 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 lattice N-vector models allowing for the leading confluent singularity. The agreement among the g-, \epsilon-, and strong-coupling expansion results is good for all N. However, at N=0,1, \epsilon- and strong-coupling expansion favor values of g^* which are sligthly lower than those obtained by the resummation of the g-expansion assuming analyticity in the Callan-Symanzik beta-function.

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