I'm not sure that you could say that the Roman Empire expanded based on ideas. The legions certainly had a fair amount to do with it, although the basis of the expansion was certainly based on ideas (as are most expansions....look at Manifest Destiny for one example). Hitler also tried to fight an idea (Bolshevism) with an idea (Nazism), although his was also certainly framed and underpinned by racial ideas as well (which could also be seen in a way as an idea fighting an idea).
As for the study of history...you'll find so many shifts in this that it's hard to track them all. Military history has certainly gone through periods where it focused on maneuvers at a higher level instead of ideas, although that does also shift over time (look at some of the recent scholarship regarding the ideals of the men who fought the Civil War for some good examples of this).
I think for your best examples of ideas fighting ideas you need to turn to politics. That is, after all, what they do on a day-to-day basis. The Green movement might also repay study, as their struggles are often in the realm of ideas (as are the anti-globalists...and I feel both groups have contributed much in terms of organization ideas and methods to the network-centric terrorist organizations we see with AQ and others).
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