Study of the dynamic behavior of Niedermayer's algorithm

We calculate the dynamic exponent for the Niedermayer algorithm applied to the two-dimensional Ising and $XY$ models, for various values of the free parameter $E_0$. For $E_0=-1$ we reobtain the Metropolis algorithm and for $E_0=1$ we regain the Wolff algorithm. For $-1\widetilde{L}$, the Niedermayer algorithm is equivalent to the Metropolis one, i.e, they have the same dynamic exponent. For a given size $L$, the correlation time is always greater for the Niedermayer algorithm than for Wolff's. For $E_0>1$, the mean size of the islands of turned spins grows faster than a power of $L$ and the correlation time is always greater than for the Wolff algorithm. Therefore, we show that the best choice of cluster algorithm is the Wolff one, when compared to the Nierdermayer generalization. We also obtain the dynamic behavior of the Wolff algorithm: although not conclusive, we propose a scaling law for the dependence of the correlation time on $L$.