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Updated: Aug 11, 2026

Modeling and Imaging 3-Dimensional Collective Cell Invasion
Published on: December 7, 2011
Invaded cluster simulations of the XY model in two and three dimensions
I Dukovski1, J Machta, L V Chayes
1Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003-3720, USA.
Abstract:
The invaded cluster algorithm is used to study the XY model in two and three dimensions up to sizes 2000(2) and 120(3), respectively. A soft spin O(2) model, in the same universality class as the three-dimensional XY model, is also studied. The static critical properties of the model and the dynamical properties of the algorithm are reported. The results are K(c)=0.454 12(2) for the three-dimensional XY model and eta=0.037(2) for the three-dimensional XY universality class. For the two-dimensional XY model the results are K(c)=1.120(1) and eta=0.251(5). The invaded cluster algorithm does not show any critical slowing for the magnetization or critical temperature estimator for the two-dimensional or three-dimensional XY models.
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