My efforts have been focused on the Edwards-Anderson spin glass in 2D, a very simple model that nevertheless exhibits very striking behavior. It contains the two critical ingredients necessary for a large degeneracy in the ground state: frustration and disorder.

The first part of my work focused on developing an algorithm to determine all the ground states of a given bond realization. For a 2D system, it is known that a single ground state can be determined in polynomial time by converting the spin glass ground state problem to the problem of finding a minimal matching of an associated graph. By extending this algorithm, I was able to develop an efficient algorithm to find all the ground states of a given realization.

Knowing all the ground states allows one to characterize the system in a systematic way that was not previously possible. Also, it is relatively easy to study the effect of small perturbations when all the ground states are known. We considered the effect of two perturbations: a quantum one equivalent to introducing a transverse field, and a classical one involving a compressible lattice and a coupling between the lattice and the bond interaction strength.

The quantum perturbation has yielded some surprising results. Although the quantum ground state is made up of a complicated superposition of classical ground states, the dynamical susceptibility exhibits sharp resonances similar to those found for single spins. We also compared the quantum ground state to that of a random undirected bipartite graph and found that it differs significantly, implying that interactions play a key role.

Papers

"Dynamics of a Complex Quantum Magnet"; JWL and S. N. Coppersmith; cond-mat/0301251

"Ground states of two-dimensional ±J Edwards-Anderson spin glasses"; JWL and S. N. Coppersmith; Phys. Rev. B 65, 134404 (2002); cond-mat/0109136

Funding Sources

This work was supported by the MRSEC program of the National Science Foundation under Award No. DMR-9808595 at The University of Chicago, by the Petroleum Research Fund of the American Chemical Society, and by the National Science Foundation under Award No. DMR-0209630. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.