On the ground state of the infinite-range Ising spin glass

Abstract

The authors investigate by direct enumeration of all states for small systems the projection of the ground state of the infinite-range Ising spin glass onto the eigenvectors of the interaction matrix Jij. They find that the largest projection (which is usually for the eigenvector corresponding to the largest eigenvalue) varies as N-0.19, where N is the number of spins. This is close to Sompolinsky's recent prediction (1981) of N -16/.