Mean field and corrections for the Euclidean minimum matching problem

The minimum matching of N random points in d-dimensional Euclidean space is a tractable model of frustration with disorder. We use numerical simulations to obtain precise estimates of the ground-state energy for 2 less than or equal to d less than or equal to 10. We then consider the approximation where distance correlations are neglected. This model's solution leads to an excellent ''random link'' approximation at d greater than or equal to 2. Incorporating three-link correlations improves the accuracy, leading to a relative error of 0.4% at d = 2 and 3. Finally, we argue that the Euclidean model's lid series is beyond all orders of a link correlation expansion.