Vertex Models and Quantum Spin Systems: a nonlocal approach

Within a general cluster framework, we discuss the loop-algorithm, a new type of cluster algorithm that reduces critical slowing down in vertex models and in quantum spin systems. We cover the example of the 6-vertex model in detail. For the F-model, we present numerical results that demonstrate the effectiveness of the loop algorithm. We discuss how to modify the original algorithm for some more complicated situations, especially for quantum spin systems in one and two dimensions.