PMID: 16383919Dec 31, 2005Paper

Exact order-parameter distribution for critical mean-field percolation and critical aggregation

Physical Review Letters
R Botet, Marek Płoszajczak

Abstract

We show that the order-parameter distribution for the mean-field percolation at the critical point is the Kolmogorov-Smirnov distribution and that it coincides with the corresponding distribution for a mean-field aggregation process at the critical time. Both processes are known to belong to the same universality class in the sense that they share the same set of critical exponents, but percolation is at the equilibrium while the aggregation is a dynamical critical process. This shows that, in this case, the probability density for order-parameter fluctuations is universal at the critical point of the infinite lattice, independent of the hypothesis of thermodynamic equilibrium.

References

Feb 1, 1985·Physical Review. B, Condensed Matter·K BinderA P Young
Aug 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G FoltinR K Zia
Oct 6, 2000·Physical Review Letters·S T BramwellM Sellitto
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·R Botet, M Ploszajczak
May 1, 2001·Physical Review Letters·R BotetJ Frankland

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Citations

Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ricardo V Paredes, Robert Botet
May 18, 2013·Physical Review Letters·D GruyerUNKNOWN INDRA collaboration
May 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Rosalba Garcia-MillanÁlvaro Corral
Oct 16, 2016·Physical Review. E·Francesc Font-Clos, Nicholas R Moloney

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