6 research outputs found
Equivalent-neighbor percolation models in two dimensions: crossover between mean-field and short-range behavior
We investigate the influence of the range of interactions in the
two-dimensional bond percolation model, by means of Monte Carlo simulations. We
locate the phase transitions for several interaction ranges, as expressed by
the number of equivalent neighbors. We also consider the
limit, i.e., the complete graph case, where percolation bonds are allowed
between each pair of sites, and the model becomes mean-field-like. All
investigated models with finite are found to belong to the short-range
universality class. There is no evidence of a tricritical point separating the
short-range and long-range behavior, such as is known to occur for and
Potts models. We determine the renormalization exponent describing a
finite-range perturbation at the mean-field limit as . Its
relevance confirms the continuous crossover from mean-field percolation
universality to short-range percolation universality. For finite interaction
ranges, we find approximate relations between the coordination numbers and the
amplitudes of the leading correction terms as found in the finite-size scaling
analysis