In this work, we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular D -dimensional lattice has a probability q to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability 1 ? q , the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes non-equilibrium phase transitions at critical points q c that depend on the lattice dimension. These transitions are of order–disorder type, presenting the same critical exponents of the Ising model. The results also suggest that the upper critical dimension of the model is D c = 4 , as for the Ising model. From the social point of view, with increasing number of social connections, it is easier to observe a majority opinion in the population.
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机译：在这项工作中，我们研究了在存在噪声的情况下三态意见模型的临界行为。这种噪音代表独立的行为，起着社会温度的作用。规则D维晶格上的每个代理都有一个q可以独立发挥作用的概率，即，他可以独立于邻居的意见来选择自己的意见。此外，互补概率为1？ q，代理通过动力学交换与随机选择的最近邻居进行交互。我们的数值结果表明，该模型在取决于晶格尺寸的临界点q c处经历了非平衡相变。这些过渡是有序-无序类型的，呈现出与伊辛模型相同的关键指数。结果还表明，与Ising模型一样，该模型的上限临界尺寸为D c = 4。从社会的角度来看，随着社会联系数量的增加，在人群中更容易观察到多数意见。
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