P. Sarkanych, Yu. Sevinchan, M. Krasnytska, P. Romanczuk, Yu. Holovatch
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引用次数: 0
摘要
在本文中,我们按照[Sarkanych P. 等,Phys. Biol., 2023, 20,045005]中提出的统计物理学方法,研究了一个共识决策模型[HartnettA. T. 等,Phys. Rev. Lett., 2016, 116, 038701]。在这一方法中,温度被用作波动的度量,而这在最初的模型中是没有考虑到的。在此,我们讨论完整图上的模型。本文的主要目的是说明分析描述可能导致非常丰富的相位行为,而这通常是完整图所不具备的。然而,模型所考虑到的各种单体(自旋)特征--它们的不均匀性和偏置强度--导致了相当非同小可的集体效应。我们证明,后者可能以连续或突然相变的形式出现,有时还伴随着再中心和阶参数翻转行为。反过来,这可能会导致从社会决策的角度进行有吸引力的解释。我们通过数值模拟来支持分析预测。此外,虽然分析计算是在平衡统计物理学形式中进行的,但数值模拟增加了另一个动力学特征--局部非线性或个体对周围意见的顺从。这一特征似乎对接近平衡态的方式及其特征都有很大影响。
Consensus decision making on a complete graph: complex behaviour from simple assumptions
In this paper we investigate a model of consensus decision making [Hartnett
A. T., et al., Phys. Rev. Lett., 2016, 116, 038701] following a statistical
physics approach presented in [Sarkanych P., et al., Phys. Biol., 2023, 20,
045005]. Within this approach, the temperature serves as a measure of
fluctuations, not considered before in the original model. Here, we discuss the
model on a complete graph. The main goal of this paper is to show that an
analytical description may lead to a very rich phase behaviour, which is
usually not expected for a complete graph. However, the variety of individual
agent (spin) features - their inhomogeneity and bias strength - taken into
account by the model leads to rather non-trivial collective effects. We show
that the latter may emerge in a form of continuous or abrupt phase transitions
sometimes accompanied by re-entrant and order-parameter flipping behaviour. In
turn, this may lead to appealing interpretations in terms of social decision
making. We support analytical predictions by numerical simulation. Moreover,
while analytical calculations are performed within an equilibrium statistical
physics formalism, the numerical simulations add yet another dynamical feature
- local non-linearity or conformity of the individual to the opinion of its
surroundings. This feature appears to have a strong impact both on the way in
which an equilibrium state is approached as well as on its characteristics.