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arXiv 1208.4381physics.soc-phcond-mat.stat-mechcs.SI
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阿克塞尔罗德社会影响力模型的热力学对应:一维情况

A thermodynamic counterpart of the Axelrod model of social influence: The one-dimensional case

Y. Gandica, E. Medina, I. Bonalde

摘要:

我们提出了一个热力学版本的阿克塞尔罗德模型的社会影响力。在一维晶格中,热力学模型变成了一个耦合Potts模型,其成键相互作用随着位置匹配特性的增加而增加。我们分析计算了一个一维系统的热力学和临界性质,表明有序-无序相变只发生在T = 0时,与文化特征q和特征F的数量无关。一维热力学Axelrod模型属于Ising和Potts模型的同一普适类,尽管局部自由度和状态依赖的键合相互作用的内部维度的增加。我们提出了一个统一的建议,比较不同的离散1D模型的指数。与我们的哈密顿描述的比较表明,在热力学极限的原始的非平衡一维Axelrod模型与噪声的行为像一个普通的热力学一维相互作用粒子系统。

英文摘要:

We propose a thermodynamic version of the Axelrod model of social influence. In one-dimensional (1D) lattices, the thermodynamic model becomes a coupled Potts model with a bonding interaction that increases with the site matching traits. We analytically calculate thermodynamic and critical properties for a 1D system and show that an order-disorder phase transition only occurs at T = 0 independent of the number of cultural traits q and features F. The 1D thermodynamic Axelrod model belongs to the same universality class of the Ising and Potts models, notwithstanding the increase of the internal dimension of the local degree of freedom and the state-dependent bonding interaction. We suggest a unifying proposal to compare exponents across different discrete 1D models. The comparison with our Hamiltonian description reveals that in the thermodynamic limit the original out-of-equilibrium 1D Axelrod model with noise behaves like an ordinary thermodynamic 1D interacting particle system.

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