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We compute the one-loop \beta-functions describing the renormalisation of thecoupling constant \lambda and the frequency parameter \Omega for the realfour-dimensional duality-covariant noncommutative \phi^4-model, which isrenormalisable to all orders. The contribution from the one-loop four-pointfunction is reduced by the one-loop wavefunction renormalisation, but the\beta_\lambda-function remains non-negative. Both \beta_\lambda and\beta_\Omega vanish at the one-loop level for the duality-invariant modelcharacterised by \Omega=1. Moreover, \beta_\Omega also vanishes in the limit\Omega \to 0, which defines the standard noncommutative \phi^4-quantum fieldtheory. Thus, the limit \Omega \to 0 exists at least at the one-loop level.Comment: 11 pages, LaTe

The $\beta$ -function in duality-covariant non-commutative $\phi^4$ -theory