Capitalize when preceded by the name of a country (as long as army is
part of the official name) or when the name is well established:
States Army British Eighth Army
Russian Army Red Army
but Israeli army, Japanese army (army is descriptive in these instances, not the official name)
When army is used by itself, capitalize in references to the U.S.
Army, but lowercase such references to any foreign army.
units through Tenth.
United States Army, the Army, Army officer
the 19th Army, the army
the Indian Army, the army, army officer
Red Army, the army
Union Army, Grant's army, Confederate Army
Army of the Potomac, the army