同质总体中社会影响下的耦合伊辛模型和相互依赖离散选择
Coupled Ising models and interdependent discrete choices under social influence in homogeneous populations
摘要：
使用统计物理学研究社会科学问题的动机和它的当前状态的艺术简要回顾，特别是离散的选择决策的情况下。两个二进制选择的耦合进行了一些详细的研究，使用伊辛模型的每个决策变量（意见或选择的时刻或自旋，社会经济等效的磁矩或自旋）。玩具模型为两种不同类型的耦合进行了研究分析和数值平均场（无限范围）近似。这相当于考虑与采用者比例或平均磁化成比例的社会影响效应。在非局部情况下，两个自旋变量通过Weiss平均场型项耦合。在社会经济背景下，当研究两个不同群体的个体时，这可能是有用的，在他们自己群体的社会影响下做出相同的决定，当他们的结果受到另一个群体的采纳者比例的影响时。在局部情况下，两个自旋变量仅通过每个个体耦合。这是考虑到一个群体中的每个人都做出了两个相互影响的不同选择。在这两种情况下，仅考虑恒定（内部和内部）耦合和外部场，即，只有完全同质的人群。大部分的结果是零场的情况下，即没有外部性或私人公用事业。相图和他们在社会经济背景下的解释进行了讨论，并与解耦的情况下。这两个系统具有许多共同的特征，包括一阶和二阶相变、亚稳态和滞后。最后，给出了一些一般性的评论，指出了这些模型的局限性，并提出了进一步的改进。
英文摘要：
The use of statistical physics to study problems of social sciences is motivated and its current state of the art briefly reviewed, in particular for the case of discrete choice making. The coupling of two binary choices is studied in some detail, using an Ising model for each of the decision variables (the opinion or choice moments or spins, socioeconomic equivalents to the magnetic moments or spins). Toy models for two different types of coupling are studied analytically and numerically in the mean field (infinite range) approximation. This is equivalent to considering a social influence effect proportional to the fraction of adopters or average magnetisation. In the nonlocal case, the two spin variables are coupled through a Weiss mean field type term. In a socioeconomic context, this can be useful when studying individuals of two different groups, making the same decision under social influence of their own group, when their outcome is affected by the fraction of adopters of the other group. In the local case, the two spin variables are coupled only through each individual. This accounts to considering individuals of a single group each making two different choices which affect each other. In both cases, only constant (intra- and inter-) couplings and external fields are considered, i.e., only completely homogeneous populations. Most of the results presented are for the zero field case, i.e. no externalities or private utilities. Phase diagrams and their interpretation in a socioeconomic context are discussed and compared to the uncoupled case. The two systems share many common features including the existence of both first and second order phase transitions, metastability and hysteresis. To conclude, some general remarks, pointing out the limitations of these models and suggesting further improvements are given.
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