论文标题
海德在三合会互动下的平衡
Heider Balance under Disordered Triadic Interactions
论文作者
论文摘要
Heider平衡解决了三体相互作用的假设，即三合会在网络的动力学中同样重要。在许多网络中，关系没有相同的强度，因此三合会的权重不同。现在，问题是，社交网络如何减少三角形的数量在加权时如何发展？结果是否可以根据我们从未加权的平衡中学到的知识进行预见？为了找到解决方案，我们考虑了一个完全连接的网络，其中三合会分配了不同的随机权重。权重来自平均$μ$的高斯概率分布和差异$σ$。我们在两个方案中研究了该系统：（\ rn {1}）$ \fracμσ\ ge 1 $的比率对应于弱障碍（小方差），即三合会的重量大致相同，（\ rn {2}）$ \ \ \ \fracμσ<1 <1 <1 <1 $ $ $ $ $ $ $ $ $ $变化（大方差）和权重多样。我们的意图是研究这种网络的结构演变。我们认为疾病在确定系统的临界温度方面起着关键作用。使用平均场方法为系统提供分析解决方案表示系统经历一阶相变。对于弱障碍，我们的仿真结果显示系统达到了全局最小值，随着温度的降低，对于高级疾病，我们设法在三合会相互作用中看到了Seudo-Kondo效应。近藤效应解释了由于低温下磁性杂质引起的金属电阻率的异常增加。在第二条制度的工作中，在我们的工作中的能量与温度中也可以看到类似的行为，并且该系统未达到全球最小值。
The Heider balance addresses three-body interactions with the assumption that triads are equally important in the dynamics of the network. In many networks, the relations do not have the same strength so, triads are differently weighted. Now, the question is how social networks evolve to reduce the number of unbalanced triangles when they are weighted? Are the results foreseeable based on what we have already learned from the unweighted balance? To find the solution, we consider a fully connected network in which triads are assigned with different random weights. Weights are coming from Gaussian probability distribution with mean $μ$ and variance $σ$. We study this system in two regimes : (\RN{1}) the ratio of $\fracμσ \ge 1 $ corresponds to weak disorder (small variance) that triads' weight are approximately the same, (\RN{2}) $\fracμσ < 1 $ counts for strong disorder (big variance) and weights are remarkably diverse. Investigating the structural evolution of such a network is our intention. We see disorder plays a key role in determining the critical temperature of the system. Using the mean-field method to present an analytic solution for the system represents that the system undergoes a first-order phase transition. For weak disorder, our simulation results display the system reaches the global minimum as temperature decreases whereas for high disorder we manage to see a seudo-Kondo effect in triadic interactions. The Kondo effect explains the anomalous increase in electrical resistivity of metals due to magnetic impurities at low temperatures. Similar behavior is seen in the energy versus temperature in our work for the second regime and the system does not reach a global minimum.
