正方形格上多数投票模型的意见域统计
Statistics of opinion domains of the majority-vote model on a square lattice
摘要：
不同文化的并列区域的存在，尽管事实上，人们的信仰有一种趋势，成为更相似的，因为个人的互动反复是一个令人困惑的现象，在社会科学。在这里，我们研究一个极端版本的频率依赖偏差模型的社会影响力，其中一个人采用的意见，其扩大的邻居，其中包括个人本身的大多数成员共享。这是多数投票模型的一个变体，在多数投票模型中，如果邻居的意见一致，个人保留自己的意见。我们假设个体固定在线性尺寸$L$的正方形晶格中，并且它们只与最近的邻居相互作用。在一个平均场的框架内，我们推导出的运动方程的密度的个人采用一个特定的意见，在单站点和对近似。虽然单点近似预测一个单一的意见域，接管整个晶格，对近似产生一个定性正确的图片与共存的不同的意见域和强烈的依赖于初始条件。广泛的蒙特卡罗模拟表明存在丰富的意见域或集群的分布，其数量与$L^2$增长，而最大的集群的大小与$\ln L^2$增长。的意见域的大小的分析表明，它们服从幂律分布的大小不太大，但它们是指数分布的限制非常大的集群。此外，类似于其他著名的社会影响力模型-阿克塞尔罗德的模型-我们发现，这些意见域是不稳定的热噪声的影响。
英文摘要：
The existence of juxtaposed regions of distinct cultures in spite of the fact that people's beliefs have a tendency to become more similar to each other's as the individuals interact repeatedly is a puzzling phenomenon in the social sciences. Here we study an extreme version of the frequency-dependent bias model of social influence in which an individual adopts the opinion shared by the majority of the members of its extended neighborhood, which includes the individual itself. This is a variant of the majority-vote model in which the individual retains its opinion in case there is a tie among the neighbors' opinions. We assume that the individuals are fixed in the sites of a square lattice of linear size $L$ and that they interact with their nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single opinion domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinion domains and a strong dependence on the initial conditions. Extensive Monte Carlo simulations indicate the existence of a rich distribution of opinion domains or clusters, the number of which grows with $L^2$ whereas the size of the largest cluster grows with $\ln L^2$. The analysis of the sizes of the opinion domains shows that they obey a power-law distribution for not too large sizes but that they are exponentially distributed in the limit of very large clusters. In addition, similarly to other well-known social influence model -- Axelrod's model -- we found that these opinion domains are unstable to the effect of a thermal-like noise.
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