Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass
Matteo Palassini, A. P. Young
Abstract
We study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from the boundary goes to zero with the (linear) size of the system L like L-lambda, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to d-df where d (=2) is the dimension of the system and df is the fractal dimension of a domain wall induced by changes in the boundary conditions. Our value for df is consistent with earlier estimates. These results show that, at zero temperature, there is only a single pure state (plus the state with all spins flipped) in agreement with the predictions of the droplet model.
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