From discrete to continuous percolation in dimensions 3 to 7. (24th October 2016)

• Record Type: Journal Article
• Authors: Koza, Zbigniew; Poła, Jakub
• Is Part Of: Journal of statistical mechanics. (2016:Oct.)
• Publication Date: 2016-10-24
• Subjects: 4 -- 3; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2016/10/103206
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency with a universal exponent θ = 3 / 2 . This allows us to estimate the continuous percolation thresholds in a model of aligned hypercubes in dimensions d = 3, …, 7 with accuracy far better than that attained using any other method before. We also report improved values of the correlation length critical exponent ν in dimensions d = 4, 5 and the values of several universal wrapping probabilities for d = 4, …, 7 .