title: Red-bond exponents of the critical and the tricritical Ising model in three dimensions.
abstract: Using the Wolff and geometric cluster algorithms and finite-size scaling analysis, we investigate the critical Ising and the tricritical Blume-Capel models with nearest-neighbor interactions on the simple-cubic lattice. The sampling procedure involves the decomposition of the Ising configuration into geometric clusters, each of which consists of a set of nearest-neighboring spins of the same sign connected with bond probability p. These clusters include the well-known Kasteleyn-Fortuin clusters as a special case for p=1-exp(-2K) , where K is the Ising spin-spin coupling. Along the critical line K=Kc , the size distribution of geometric clusters is investigated as a function of p . We observe that, unlike in the case of two-dimensional tricriticality, the percolation threshold in both models lies at pc =1-exp(-2Kc) . Further, we determine the corresponding red-bond exponents as yr =0.757(2) and 0.501(5) for the critical Ising and the tricritical Blume-Capel models, respectively. On this basis, we conjecture yr =1/2 for the latter model.
authors.affiliation: Faculty of Applied Sciences, Delft University of Technology, P. O. Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: Youjin
authors.initials: Y
authors.lastname: Deng
authors.forename: Henk W J
authors.initials: HW
authors.lastname: Blöte