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In the corrupted compass model on a vertex-transitive graph, a neighbouringedge of every vertex is chosen uniformly at random and opened. Additionally,with probability $p$, independently for every vertex, every neighbouring edgeis opened. We study the size of open clusters in this model. Hirsch et al. haveshown that for small $p$ all open clusters are finite almost surely, while forlarge $p$, depending on the underlying graph, there exists an infinite opencluster almost surely. We show that the corresponding phase transition issharp, i.e., in the subcritical regime, all open clusters are exponentiallysmall. Furthermore we prove a mean-field lower bound in the supercriticalregime. The proof uses the by now well established method using the OSSSinequality. A second goal of this note is to showcase this method in anuncomplicated setting.

Sharpness of the Phase Transition for the Corrupted Compass Model on Transitive Graphs