A Swendsen-Wang update algorithm for the Symanzik improved sigma model

We study a generalization of Swendsen-Wang algorithm suited for Potts models with next-next-neighborhood interactions. Using the embedding technique proposed by Wolff we test it on the Symanzik improved bidimensional non-linear $\sigma$ model. For some long range observables we find a little slowing down exponent ($z\simeq 0.3$) that we interpret as an effect of the partial frustration of the induced spin model.