Ground state of quantum spin glasses with infinite range interactions

Alain H. Billoire

Konrad H. Fischer

Hidetoshi Nishimori, Y‐h. Taguchi, Takehiko Oguchi

We have investigated the spin-1/2 random Heisenberg model with infinite range interactions by a numerical method. Extrapolation of finite size ( N ≦16) properties to the infinite system has yielded the following results. The average ground state energy is lower than that of the SK model (Ising spin) by about 25%. In the ground state, a critical point between the spin glass and ferromagnetic (mixed) phases exists just around the critical point (\(\tilde{J}_{0}/\tilde{J}{=}1\)) of the corresponding classical random Heisenberg model. Quantum fluctuations are concluded not to change the ground state properties qualitatively.

N. I. Lebedev

Bosiljka Tadić, R. Pirc, R. Blinc +1 more

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/.