I rent to people. Standard lease agreements specify no illegal activities. Illegal activities are grounds for immediate eviction, But I can't tell you weather it will take them 1 Day or 30. That depends on your state "tenant & landlord rights". Some states favor landlord while others favor tenant.
You are within your rights to cancel the lease. But step one is to make it clear that its them or you. Your a good tenant that doesn't have to put up with this crap, These tenants next door sound like a landlords plague. If your realty company has any brains they will work 100% on your side with-out revealing that your behind the complaint.