Discipline?

[Ludens]

Discipline does big 2 things that I can remember. Discipline will help prevent troops from charging without orders. Also with spearclass troops higher disciplined units are suppose to be able hold there formation better. And I think all disciplined units do'nt lose morale(greatly reduced) upon generals death and get a minor morale hit (instead of a big 1) when non elite unir\ts route

This is quite right (except that disciplined units are not very worried by non-elite, non-disciplined units routing), but it is debatable whether the militairy academy actually makes all units disciplined. I have never seen any evidence of it. I may perhaps do the same thing as the drill dojo: troops keep their formation better and are easier to rally, but otherwise there was no effect.

[katank]

it says +1 discipline but it seems it's not enough to actually give it a disciplined tag if not already disciplined so not much tangible benefits.

I'd say academy isn't really that useful unless you are playing as the Turks

[lars573]

Here is what the total war begginers guide says about discipline

Disciplined means the unit is less likely to chase off after enemy units when it is in the impetuous morale state. It also means that the unit doesn't care about routing units on its own side unless they are of disciplined or elite status. The death of your general also has a reduced effect on disciplined units morale. This means that routing peasants and the like can no longer panic your army. If a unit does not possess disciplined status by default the only way to add it is to build the military academy in one of your production provinces. This will not add the disciplined tag to your unit but it will increase their discipline slightly. Units like knights still tend to be impetuous even with the discipline upgrade.

And in the NTW mod there are 2 building that give a discipline bonus the military academy (discipline +1) which the modders moved from the top of the tech tree to the bottom, you can build it when you build the mods version of a fort. When you get to the mods castle level you can build a colledge of officers that gives a +3 discipline bonus.