Nyczka Piotr, Sznajd-Weron Katarzyna, Cisło Jerzy
Institute of Theoretical Physics, University of Wrocław, pl Maxa Borna 9, 50-204 Wrocław, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011105. doi: 10.1103/PhysRevE.86.011105. Epub 2012 Jul 5.
We study a nonlinear q-voter model with stochastic driving on a complete graph. We investigate two types of stochasticity that, using the language of social sciences, can be interpreted as different kinds of nonconformity. From a social point of view, it is very important to distinguish between two types nonconformity, so-called anticonformity and independence. A majority of work has suggested that these social differences may be completely irrelevant in terms of microscopic modeling that uses tools of statistical physics and that both types of nonconformity play the role of so-called social temperature. In this paper we clarify the concept of social temperature and show that different types of noise may lead to qualitatively different emergent properties. In particular, we show that in the model with anticonformity the critical value of noise increases with parameter q, whereas in the model with independence the critical value of noise decreases with q. Moreover, in the model with anticonformity the phase transition is continuous for any value of q, whereas in the model with independence the transition is continuous for q ≤ 5 and discontinuous for q>5.
我们研究了在完全图上具有随机驱动的非线性q-投票者模型。我们研究了两种类型的随机性，用社会科学的语言来说，它们可以被解释为不同类型的不遵从。从社会角度来看，区分两种类型的不遵从，即所谓的反遵从和独立性，是非常重要的。大多数工作表明，在使用统计物理工具的微观建模方面，这些社会差异可能完全无关紧要，并且两种类型的不遵从都起着所谓社会温度的作用。在本文中，我们阐明了社会温度的概念，并表明不同类型的噪声可能导致定性上不同的涌现性质。特别是，我们表明在具有反遵从的模型中，噪声的临界值随参数q增加，而在具有独立性的模型中，噪声的临界值随q减小。此外，在具有反遵从的模型中，对于任何q值，相变都是连续的，而在具有独立性的模型中，当q≤5时转变是连续的，当q>5时转变是不连续的。
