论文标题
旋转系统和简单液体中反问题的图表学
Diagrammatics for the Inverse Problem in Spin Systems and Simple Liquids
论文作者
论文摘要
建模复杂的系统，例如神经网络，简单的液体或鸟类群，通常与教科书相反：已知平均值和相关性的数据，我们试图找到与其一致的给定模型的参数。通常，没有直接从模型中进行确切的计算，我们将采用昂贵的数值方法。一种特殊的情况是具有连续自由度的多项式校正的扰动高斯模型的情况。实际上，在过去的60年中，已经实施了此案的扰动扩展。但是，有一些模型是，确切可解决的部分是非高斯的，例如田间独立旋转或理想的颗粒气体。我们在非高斯但可解决的概率权重的弱相关性中实施了示意性扰动方案。这特别适用于具有弱耦合的自旋模型（Ising，Potts，Heisenberg），或具有弱相互作用电势的简单液体。我们的方法施放具有离散自由度的系统以及在相同理论框架内具有连续的系统。当核心理论是高斯时，它将减少到著名的Feynman图表学。
Modeling complex systems, like neural networks, simple liquids or flocks of birds, often works in reverse to textbook approaches: given data for which averages and correlations are known, we try to find the parameters of a given model consistent with it. In general, no exact calculation directly from the model is available and we are left with expensive numerical approaches. A particular situation is that of a perturbed Gaussian model with polynomial corrections for continuous degrees of freedom. Indeed perturbation expansions for this case have been implemented in the last 60 years. However, there are models for which the exactly solvable part is non-Gaussian, such as independent Ising spins in a field, or an ideal gas of particles. We implement a diagrammatic perturbative scheme in weak correlations around a non-Gaussian yet solvable probability weight. This applies in particular to spin models (Ising, Potts, Heisenberg) with weak couplings, or to a simple liquid with a weak interaction potential. Our method casts systems with discrete degrees of freedom and those with continuous ones within the same theoretical framework. When the core theory is Gaussian it reduces to the well-known Feynman diagrammatics.
