The structure of enumerated spin glass state spaces

Tilla Klotz, Sven Schubert, K. H. Hoffmann

Sven Schubert, K. H Hoffmann

\n \nAging phenomena are observed in many spin class experiments.\nHeuristic state space models were presented in the past to\nreproduce these effects. We here start the investigation by\nconsidering the real state space of an Ising spin glass\nHamiltonian. A branch-and-bound algorithm is used to find the\nlow-energy part of the state space. We solve the problem of the\nstill huge size of the state space by employing a special\ncoarse-graining algorithm. The system can be reduced to a\ncomputational treatable size. We demonstrate that these systems\nstill contain all properties necessary for aging effects.\n\n

Haim Sompolinsky, Annette Zippelius

Scott Kirkpatrick, A. P. Young

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 J ij . 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 -1 6/.

Yukiyasu Ozeki, Nobuyasu Ito, Keita Ogawa

Numerical evidence that the number of pure states in the spin glass phase is infinite near the ferromagnetic phase boundary for the three dimensional (3D) ± J Ising model and 3D gauge glass models is presented. It is consistent with the mean field theory which suggests the multivalley structure of the spin glass phase. We will show that the onset of the ferromagnetic long-range order and that of the ferromagnetic spontaneous symmetry breaking do not coincide with each other, and this phenomenon characterizes the structure of the phase space.