Absence of Ordering in Short Range Vector Spin Glass: Revisited

Abstract

We show the absence of spin glass ordering in short range vector spin systems with random symmetric exchange interactions in spatial dimension d ≤4. The argument is an improvement of our previous theory; we circumvent the use of the unproved assumption which has been shown not to hold by O'Neill and Moore. Still, we have not completed a mathematically rigorous proof because of the use of the replica method and of the unproved clustering property of spin correlation functions.