  From the work of Dervan-Keller, there exists a quantization of the critical
equation for the J-flow. This leads to the notion of J-balanced metrics. We
prove that the existence of J-balanced metrics has a purely algebro-geometric
characterization in terms of Chow stability, complementing the result of
Dervan-Keller. We also obtain various criteria that imply uniform J-stability
and uniform K-stability. Eventually, we discuss the case of K\"ahler classes
that may not be integral over a compact manifold.
