论文标题
在寻找社交滞后 - 对称阈值模型，具有独立性
In search for the social hysteresis -- the symmetrical threshold model with independence on Watts-Strogatz graphs
论文作者
论文摘要
我们通过对瓦特 - strogatz图上的成对近似和蒙特卡洛模拟来研究具有独立性（噪声）的同质对称阈值模型。该模型是著名Granovetter阈值模型的修改版本：概率$ p $，选民独立行动，即随机采用两个状态之一+/-；有了补充概率$ 1-p $，选民会采用给定的州，如果足够大的部分（高于给定的阈值R）在其附近的个人处于该州。我们表明，由噪声参数P引起的相变的特征取决于阈值R以及图参数。对于r = 0.5，仅观察到连续的相变，而对于r> 0.5，也可能是不连续的相变。磁滞随着平均程度<k>和重写参数beta的增加而增加。另一方面，滞后宽度与阈值$ r $之间的依赖性是非单调的。观察到最大滞后的R的值，与描述性规范的大多数大小重叠，以便在社会实验中操纵人员。我们将本文中获得的结果在更广泛的情况下获得，并在其他两种二进制观点模型的背景下进行讨论，即多数投票和Q-Voter模型。
We study the homogeneous symmetrical threshold model with independence (noise) by pair approximation and Monte Carlo simulations on Watts-Strogatz graphs. The model is a modified version of the famous Granovetter's threshold model: with probability $p$ a voter acts independently, i.e. takes randomly one of two states +/-; with complementary probability $1-p$, a voter takes a given state, if sufficiently large fraction (above a given threshold r) of individuals in its neighborhood is in this state. We show that the character of the phase transition, induced by the noise parameter p, depends on the threshold r, as well as graph's parameters. For r=0.5 only continuous phase transitions are observed, whereas for r>0.5 also discontinuous phase transitions are possible. The hysteresis increases with the average degree <k> and the rewriting parameter beta. On the other hand, the dependence between the width of the hysteresis and the threshold $r$ is non-monotonic. The value of r, for which the maximum hysteresis is observed, overlaps pretty well the size of the majority used for the descriptive norms in order to manipulate people within social experiments. We put results obtained within this paper in a broader picture and discuss them in the context of two other models of binary opinions, namely the majority-vote and the q-voter model.
