Testing validity of the Kirkwood approximation using an extended Sznajd model

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
André M Timpanaro, Serge Galam

Abstract

We revisit the deduction of the exit probability of the one-dimensional Sznajd model through the Kirkwood approximation [F. Slanina et al., Europhys. Lett. 82, 18006 (2008)EULEEJ0295-507510.1209/0295-5075/82/18006]. This approximation is peculiar in that, in spite of the agreement with simulation results [F. Slanina et al., Europhys. Lett. 82, 18006 (2008)EULEEJ0295-507510.1209/0295-5075/82/18006; R. Lambiotte and S. Redner, Europhys. Lett. 82, 18007 (2008)EULEEJ0295-507510.1209/0295-5075/82/18007; A. M. Timpanaro and C. P. C. Prado, Phys. Rev. E 89, 052808 (2014)PLEEE81539-375510.1103/PhysRevE.89.052808], the hypothesis about the correlation lengths behind it are inconsistent and fixing these inconsistencies leads to the same results as a simple mean field. We use an extended version of the Sznajd model to test the Kirkwood approximation in a wider context. This model includes the voter, Sznajd, and "United we stand, divided we fall" models [R. A. Holley and T. M. Liggett, Ann. Prob. 3, 643 (1975)APBYAE0091-179810.1214/aop/1176996306; K. Sznajd-Weron and J. Sznajd, Int. J. Mod. Phys. C 11, 1157 (2000)IJMPEO0129-183110.1142/S0129183100000936] as different parameter combinations, meaning that some analytical results from these m...Continue Reading

References

Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Claudio Castellano, Romualdo Pastor-Satorras
Nov 9, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Piotr PrzybyłaMaciej Tabiszewski
Oct 30, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·André M Timpanaro, Carmen P C Prado
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·André M Timpanaro, Serge Galam

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