Percolation properties of the Wolff clusters in planar triangular spin models.

We formulate the Wolff algorithm as a site-bond percolation problem, apply it to the ferromagnetic and antiferromagnetic planar triangular spin models, and study the percolation critical behavior using Anite-size scaling. In the former case the Wold' algorithm is successful as an accelerating algorithm, whereas in the latter case it is not. We found the percolation temperatures and the cluster exponents for both models. In the antiferrornagnetic model, the percolation temperature is higher than the critical temperature of the spin system. The cluster exponents are found to be the same as the random two-dimensional (2D) percolation. In the ferromagnetic model, the percolation temperature agrees with the critical temperature, and the cluster exponents are dift'erent from the random 2D percolation, meaning that they are in di6'erent universal classes. For the ferromagnetic model we discuss the mechanism of the cluster growth in the regime of the Kosterlitz-Thouless transition. We also note a relation between the dynamic exponent and the percolation exponents.