Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus.

  title={Critical exponents for the homology of Fortuin-Kasteleyn clusters on a torus.},
  author={Alexi Morin-Duchesne and Yvan Saint-Aubin},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={80 2 Pt 1},
A Fortuin-Kasteleyn cluster on a torus is said to be of type {a,b},a,b in Z , if it is possible to draw a curve belonging to the cluster that winds a times around the first cycle of the torus as it winds -b times around the second. Even though the Q -Potts models make sense only for Q integers, they can be included into a family of models parametrized by beta = square root of Q for which the Fortuin-Kasteleyn clusters can be defined for any real beta(0,2] . For this family, we study the… 

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