In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C/rd+Ï, where r is the distance length between distinct sites and d=1. We introduce and test an order-N Monte Carlo algorithm and we determine as a function of Ï the critical value Cc at which percolation occurs. The critical exponents in the range 0<Ï<1 are reported. Our analysis is in agreement, up to a numerical precision â10-3, with the mean-field result for the anomalous dimension Î·=2-Ï, showing that there is no correction to Î· due to correlation effects. The obtained values for Cc are compared with a known exact bound, while the critical exponent Î½ is compared with results from mean-field theory, from an expansion around the point Ï=1 and from the expansion used with the introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with Ï>0.
|Titolo:||One-dimensional long-range percolation: A numerical study|
|Autori:||Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.|
|Data di pubblicazione:||2017|
|Numero di Articolo:||012108|
|Digital Object Identifier (DOI):||10.1103/PhysRevE.96.012108|
|Appare nelle tipologie:||1.1 Journal article|