Critical Correlation Function and Exponentη: A Sum Rule

A sum rule is derived from the connection of the critical specific heat with the critical correlation function in the disordered symmetric state. The "Ornstein-Zernike hole" which appears above the critical point must, by virtue of this sum rule, be canceled exactly by the "Fisher-Langer tail." It follows that the anomalous dimension index η is fixed by the shape of the spectral function. A spectral function satisfying certain general properties yields η≈0.04.