i've heard [but not read] that the famous german historian, hans delbruck debunks the whole hundreds of thousands or millions of men army stats quite nicely due to logisitics.

example:
say you have a million man force that eat a million pounds of wheat a day, you would need an wagon train of 100,000 oxen to feed them. and the wagon train itself would need to consume 1 million pounds of wheat, just for it to be able to transport the million pounds of wheat for the army. so we're talking about 60 million pounds of wheat for that army for one month. and for that army to be able to actually move, they would need to have depots of 60 million pounds of wheat spaced out a month apart, and there is no way the persians had anywhere near that kind of food surplus. otherwise any army that assembled of that magnitude, would starve within 3 days. delbruck reputedly did the stats work of what an army like that would need and concluded that in no way could herodetus' numbers be close to the truth. again, i have not read delbruck, but that is my understanding of his work.