Generalized cluster algorithms for frustrated spin models

Standard Monte Carlo cluster algorithms have proven to be very effective for many different spin models. However, they fail for frustrated spin systems. Recently, a generalized cluster algorithm was introduced that works extremely well for the fully frustrated Ising model on a square lattice by placing bonds between sites based on information from plaquettes rather than links of the lattice. Here we study some properties of this algorithm and some variants of it. We introduce a practical methodology for constructing a generalized cluster algorithm for a given spin model, and apply this method to some other frustrated Ising models. We find that such algorithms work well for simple fully frustrated Ising models in two dimensions, but appear to work poorly or not at all for more complex models such as spin glasses.