It's secession!
Sorry, pet peeve of mine.
As for an objectivist state, I suppose one could consult the writings or Terry Goodkind since his books are all about an Objectivist setting up an empire in a fantasy world. The end result is ... rather horrifying, with the Objectivist "hero" doing things like butchering a group of unarmed anti-war protestors on the grounds that they "hate moral clarity."
He doesn't seem to understand objectivism, or at least libertarianism, then, confusing it with "far-right" movements like Fascism. Libertarian ideology is to avoid war as much as possible. It is, by definition, an inefficient enterprise, and, (even worse!), serves to promote higher taxes, central planning, and the interests of the state (big government!). No "true" Objectivist or Libertarian state would ever go to war unless its very survival is threatened.
Getting off of philosophy, an objectivist state of any significance is unlikely. It, ironically, shares many similarities with the "final development" of Communism, because it assumes that everyone will be willing and eager to work towards a greater good. Libertarianism, however, is more pragmatic, because it applies the economic principle of the "invisible hand," that when people work in their own interests, they are also working in the interest in the greater good.
I think, that with fairly minimal tomfoolery, if you butterfly away Karl Marx, World War I, and the Great Depression, the US or UK might become Libertarian. Or you could just have Ross Perot become POTUS in 1992.