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Some will, and some wont accept you without a referral.  The one I go to does require a referral, as they are the largest rx'er of narcotics in the state.  It is an "end of the line" clinic, for patients who have not responded to non-opiod treatments.

The problem you will most likely encounter is insurance.  Very few insurance providers will cover a visit to a specialist without a referral from a primary care doctor first.  Some PPP's and PPO's dont reqire referrals for some specialists, but even some of these still do for pain clinics, probably because of the governments witch-hunt on narcotics prescribers and patients.  

This is the way my coverage is.  I can see many different specialist without referalls/prior authorizations, but not pain management.