Swendsen-Wang algorithm

The Swendsen-Wang algorithm divides the entire lattice into clusters in exactly the same way, with this same probability Padd of making a link. But then, instead of flipping just one cluster, each cluster is independently flipped with probability We notice the following facts about this algorithm. 

At high temperatures, the Swendsen-Wang algorithm tends to divide the lattice into very small clusters because Padd becomes small. As T -> oo... 

Comparison of Dynamic Exponent z for the Metropolis, Wolff and Swendsen-Wang Algorithms in Various Numbers of Dimensions11... 

So, how does the invaded cluster algorithm work Basically, it is just a variation of the Swendsen-Wang algorithm in which the temperature is continually adjusted to look for the critical point. The algorithm finds the fraction of links at which a percolating backbone of spins first forms across the lattice and uses this fraction to make successively better approximations to the critical temperature at each Monte Carlo step. In detail, here s how it goes ... 

Once the links are made, we flip each cluster on the lattice separately with probability just as we do in the normal Swendsen-Wang algorithm. Then the whole procedure is repeated from step 2 again. 

The results for the invaded-cluster algorithm are impressive. Machta et al. [18] found equilibration times 20 or more times faster than the Swendsen-Wang algorithm at Tc for the two- and three-dimensional Ising systems they examined, and of course, the invaded-cluster algorithm allowed them to measure the value of Tc, which is not directly possible with... 

The Swendsen-Wang algorithm can also be generalized for use with Potts models in a very simple fashion, as can all of the other algorithms described in Section III. 

---