Abstract
We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of ${L}^{3}$ spins. After averaging over large sets of EA system samples of $3\ensuremath{\le}L\ensuremath{\le}10$, we obtain accurate numbers for distributions $p(q)$ of the overlap parameter $q$ at very low-temperature $T$. We find $p(0)/T\ensuremath{\rightarrow}0.233(4)$ as $T\ensuremath{\rightarrow}0$. This is in contrast with the droplet scenario of spin glasses. We also study the number of mismatched links---between replica pairs---that come with large scale excitations. Contributions from small scale excitations are discarded. We thus obtain for the fractal dimension of outer surfaces of $q\ensuremath{\sim}0$ excitations in the EA model ${d}_{s}\ensuremath{\rightarrow}2.59(3)$ as $T\ensuremath{\rightarrow}0$. This is in contrast with ${d}_{s}\ensuremath{\rightarrow}3$ as $T\ensuremath{\rightarrow}0$ that is predicted by mean-field theory for the macroscopic limit.
Highlights
Whether spin glasses are complex systems is an important issue
For a more accurate picture of how pQ varies with L in the EA model, we show log-log plots of pQ/T vs L, for
We have reported data for p(q) from averages over large sets of EA and SK systems at very low temperature
Summary
Whether spin glasses are complex systems is an important issue. We have discussed this in some detail in Ref. 1, where we gave numerical evidence for fundamental differences between the spin-glass phases of the Edwards-Anderson (EA) and Sherrington-Kirkpatrick (SK) models. (The statistics of spikes in overlap distributions in different system samples, which have been studied by Yucesoy et al, point away from an RSB scenario, though this conclusion is criticized in Ref. 7.). A roughly constant value of p(q ∼ 0) over a 3 L 8 size range was shown to be consistent with these data This is, as in the RSB, not the droplet scenario of spin glasses. As in Ref. 15, we define fJ ml(q) as the time average of the FML (for a sample with a given set J of bonds) which is observed over all time intervals while the value of the spin overlap is q.
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