We consider the Mean Field limit of Gibbsian ensembles of 2-dimensional (2D) point vortices on the torus. It is a classical result that in such limit correlations functions converge to 1, that is, point vortices decorrelate: We compute the rate at which this convergence takes place by means of Gaussian integration techniques, inspired by the correspondence between the 2D Coulomb gas and the Sine-Gordon Euclidean field theory.

中文翻译：

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点涡系综平均场极限中相关率的衰减

我们考虑环面上二维 (2D) 点涡旋的吉布斯系综的平均场极限。这是一个经典的结果，在这种极限相关函数收敛到 1，即点涡去相关：我们通过高斯积分技术计算这种收敛发生的速率，灵感来自 2D 库仑气体和Sine-Gordon 欧几里得场论。