减少自旋系统中的挫折：作为XOR-SAT问题的社会平衡
Reducing Frustration in Spin Systems: Social Balance as an XOR-SAT problem
摘要：
Antal \emph{et al.} [ T. Antal，P. L. Krapivsky和S. Redner，Phys. Rev. E { \bf 72}，036121（2005）。].我们将它们的三元动力学推广到任意整数$k$的$k$ -圈动力学.我们推导出的相结构，确定固定的解决方案，并计算所需的时间达到冻结状态。作为$k$的函数的相结构的主要差异与$k$是偶数还是奇数有关。作为第二个推广，我们将Antal \emph{et al.}所考虑的全对全耦合稀释为连接概率为$w<1$的随机网络。...
英文摘要：
Reduction of frustration was the driving force in an approach to social balance as it was recently considered by Antal \emph{et al.} [ T. Antal, P. L. Krapivsky, and S. Redner, Phys. Rev. E {\bf 72}, 036121 (2005). ]. We generalize their triad dynamics to $k$-cycle dynamics for arbitrary integer $k$. We derive the phase structure, determine the stationary solutions and calculate the time it takes to reach a frozen state. The main difference in the phase structure as a function of $k$ is related to $k$ being even or odd. As a second generalization we dilute the all-to-all coupling as considered by Antal \emph{et al.} to a random network with connection probability $w<1$. ...
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