SIMPLICITY OF STATE AND OVERLAP STRUCTURE IN FINITE-VOLUME REALISTIC SPIN-GLASSES

We present a combination of heuristic and rigorous arguments indicatin g that both the pure state structure and the overlap structure of real istic spin glasses should be relatively simple: in a large finite volu me with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-re lated in the non-Ising case) states appear, and the Parisi overlap dis tribution correspondingly exhibits at most a pair of delta functions a t +/- q(EA). This rules out the nonstandard mean-field picture introdu ced by us earlier, and when combined with our previous elimination of more standard versions of the mean-field picture, argues against the p ossibility of even limited versions of mean-field ordering in realisti c spin glasses. If broken spin-flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet-scaling two-state picture, and the chaotic pairs many-state p icture introduced by us earlier. We present scaling arguments which pr ovide a possible physical basis for the latter picture, and discuss po ssible reasons behind numerical observations of more complicated overl ap structures in finite volumes. [S1063-651X(98)07202-X].