About the fastest growth of the Order Parameter in models of percolation

S.S. Manna

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 9, 2833-2841

Abstract: The growth of the average size 〈smax〉 of the largest component at the percolation threshold pc(N) on a graph of size N has been defined as 〈smax(pc(N),N)〉∼Nχ. Here we argue that the precise value of the ‘growth exponent’ χ indicates the nature of percolation transition; χ<1 or χ=1 determines if the transition is continuous or discontinuous. We show that a related exponent η=1−χ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the Order Parameter.

Keywords: Percolation; Order of transition; Explosive percolation (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:9:p:2833-2841

DOI: 10.1016/j.physa.2011.12.065

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