On the exit probability of the extended Sznajd model and the Kirkwood approximation

4th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Timpanaro, Andr M.^1,2 ; Galam, Serge^2

Instituto de Fsica, Universidade de so Paulo, So Paulo, Brazil^1

CEVIPOF Sciences Po, Paris, France^2

关键词: Extended versions;    Initial conditions;    Mean-field treatments;    Simple expression;    Sociophysics;    Spin models;    Sznajd model;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/633/1/012111/pdf
DOI  :  10.1088/1742-6596/633/1/012111

来源: IOP

【 摘 要 】

The Sznajd model is a spin model, inspired by sociophysics, where 2 aligned spins influence a neighbouring spin to change its orientation. A bit of controversy arised in the literature recently about the properties of its one dimensional case, namely the exit probability, the probability that the system ends up in the "all spins up" state as a function of the proportion of spins pointing up in the initial condition. The Kirkwood approximation, which is a type of mean-field treatment, gives a surprisingly simple expression for this probability that has been verified for simulations with up to 107sites. Nevertheless some aspects of the Kirkwood approximation cast doubt upon its validity. In this work, we use an extended version of the Sznajd model due to G. Kondrat, that allows for any interaction between a pair of spins and a neighbouring spin that respects the symmetry between up and down spins. Looking at the Kirkwood approximation for this case we obtain an expression for the exit probability in the cases where the "all up" state is absorbing and compare this probability with simulations, finding cases where the results are indeed not valid.