Babak Fotouhi, Michael G. Rabbat
The theory of class struggle is modeled within the framework of statistical physics. Dichotomous spin dynamics on a pyramid-shaped hierarchical structure are examined (akin to the Cayley tree). A "head node" is placed at the apex. The system embodies a number of "classes", corresponding to different levels of the hierarchy. A class is comprised of nodes that are equidistant from the head. Weighted links exist between nodes from the same and different classes. We study the effect of these weights on the dynamics. The spin (hereafter, "state") of the head node is fixed, and it imposes its state on the rest of the hierarchy. Necessary conditions so that the classes eventually repudiate or acquiesce in the state imposed by the head node are found. The results show that, to reach unanimity across the hierarchy, it suffices for the head node to make the bottom-most class adopt the same state. Then the rest of the hierarchy will inevitably comply, regardless of the inter/intra class link configurations. Hence the role of the bottom-most class is signified. This also sheds light on the importance of mass media as a means of synchronization between the top-most and bottom-most classes.
View original:
http://arxiv.org/abs/1207.7251
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