We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter $\alpha$ tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brand{a}o and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

中文翻译：

---

磁场中几乎玻色子任意子的平均场近似

我们研究了外部磁场中大量 N 个二维任意子的基态。我们考虑一个缩放限制，其中当 N 趋于无穷大时，统计参数 $\alpha$ 趋于零，这允许将统计视为“来自玻色子端的扰动”。我们的模型是磁场中的玻色子，通过每个粒子携带的磁电荷产生的长程磁势相互作用，涂抹在半径为 R 的圆盘上。 N趋于无穷大。我们使用 Brand{a}o 和 Harrow 的 de Finetti 定理的信息理论版本来证明所谓的“平均场近似”：粒子表现得像通过自洽磁场相互作用的独立、同分布的玻色子。