Numerical results for the Edwards-Anderson spin-glass model at low temperatur

Abstract

We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of L3 spins. After averaging over large sets of EA system samples of 3<= L<=10, we obtain accurate numbers for distributions p(q) of the overlap parameter q at very low-temperature T. We find p(0)/T → 0.233(4) as T → 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 ∼ 0 excitations in the EA model ds → 2.59(3) as T → 0. This is in contrast with ds → 3 as T → 0 that is predicted by mean-field theory for themacroscopic limit.