FisMat2017 - Submission - View

Abstract's title: Long to short range crossover: the case of one-dimensional percolation
Submitting author: Giacomo Gori
Affiliation: CNR-IOM Trieste, SISSA
Affiliation Address: Via Bonomea, 265. 34136, Trieste, Italy
Country: Italy
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Marco Michelangeli (SISSA, Trieste), Nicolò Defenu (Universität Heidelberg) Andrea Trombettoni (CNR-IOM, SISSA & INFN, Trieste)
Abstract

We present results on bond percolation in a one-dimensional chain with power-law bond probability C/r1+σ, where r is the distance between distinct sites. We introduce and test an order N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 < σ < 1 are reported and compared with mean-field and ε-expansion results. Our analysis is in agreement, up to a numerical precision ≈ 10-3, with the mean field result for the anomalous dimension η = 2 − σ, showing that there is no correction to η due to correlation effects.