”Article 4 – The treaty does not recognize, dispute, nor establish territorial sovereignty claims; no new claims shall be asserted while the treaty is in force;”
Not every country has signed that, but all the import ones (big powers and those who claim it because of its relative nearness to their shores) have (https://en.wikipedia.org/wiki/Antarctic_Treaty_System#Partie...). Note that the USA and Russia reserve the right to lay a claim in the future, so this is more like a (long-lasting) pause than an end state in the game.
Now, why has everybody been acting so nicely for decades? Basically because there isn’t much to fight over there (given its distance to land masses of the major powers, it isn’t even interesting for deploying military tracking stations)
I don’t see this change soon, but if it turns out that Antarctica has resources that can be mined profitably, that can change.