A new algorithm is presented, which allows to calculate numerically the partition function Z for systems, which can be described by arbitrary interaction graphs and lattices, e.g. Ising models or Potts models (for arbitrary values q>0).

The basic idea is to measure the distribution of the number of connected components in the corresponding Fortuin-Kasteleyn representation and to compare with the case of zero degrees of freedom, where the exact result Z=1 is known. As application, d=2 and d=3-dimensional ferromagnetic Potts models are studied, and from calculation of large sizes N=1000×1000, N=100x100x100, the critical values q_c(d), where the transition changes from second to first order, are determined.

The same approach can be used to study the rare-event tail of the distribution of components in Erdös-Renyi random graphs. The result is compared to analytical calculations. As application in molecular Biology, the statistics of sequence alignment is evaluated, a procedure used in huge databases to compare e.g. protein sequences.

University of Goettingen, Institute for Theoretical Physics