Non-analyticity of the Callan-Symanzik beta-function of O(N) models

Abstract

In the framework of the 1/N-expansion we show that the Callan-Symanzik beta- function associated with the four-point coupling g is non-analytic at its zero, i.e. at the fixed-point value g^* of g. This behavior can be interpreted by renormalization group arguments, and written in terms of scaling correction exponents. We obtain accurate determinations of g^* in 3-d and 2-d by exploiting two alternative approaches: the (4-d)-expansion and the high-temperature expansion. These results are compared with the available estimates by other approaches, such as the fixed-dimension perturbative expansion, Monte Carlo simulations, etc... We also present results for the n-point renormalized coupling constants that parameterize the behavior of the effective potential in the high- and low- temperature phases.

LATTICE98(spin), 3 pages

References in corpus (5)

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• High-precision determination of the critical exponent gamma for self-avoiding walks
• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
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• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• The critical equation of state of three-dimensional XY systems
• Precision calculation of universal amplitude ratios in $O(N)$ universality classes: Derivative Expansion results at order $\mathcal{O}({\partial }^4)$
• Mean-field expansion for spin models with medium-range interactions
• Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy