You should really look into the Zapatistas. They used civil justice, and were relatively stateless. Also, just because someone talks about anarchism doesn't mean they're talking about being without a process of community involved problem solving/justice. You just need to know what anarchosyndicalism is, or communitarianism, or maoism. The previous user did say "anarchism and communism" after all.
Throughout most of human history "standing armies" and "permanent police forces" didn't exist, they were formed from the community when necessary (and often merely to beat up bad bosses or known criminals).
So the whole idea that society pops out of existence without central command over violent forces - doesn't match up against most of human history.