The Wolff Algorithm
External Sources and Boundaries

Jorge L. deLyra

Department of Mathematical Physics, Physics Institute, University of São Paulo

Version 1, July 2006

We will consider here the technical question of how to implement the Wolff cluster algorithm for the Ising model in the presence of arbitrary external sources. We will also consider the use of the algorithm in lattices with fixed rather than periodical boundary conditions, as well as the use of truncated clusters. We will not deal with the technical aspects relating to how well the algorithm itself works, with respect to the elimination of the phenomenon of critical slowing down. For that, the reader is referred to the original papers on the cluster algorithms [1,2].