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Evidence for a trivial ground-state structure in the two-dimensional Ising spin glass

1999; American Physical Society; Volume: 60; Issue: 14 Linguagem: Inglês

10.1103/physrevb.60.r9919

1095-3795

Matteo Palassini, A. P. Young,

Complex Systems and Time Series Analysis

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 ${L}^{\ensuremath{-}\ensuremath{\lambda}},$ where $\ensuremath{\lambda}=\ensuremath{-}0.70\ifmmode\pm\else\textpm\fi{}0.08.$ We argue that $\ensuremath{\lambda}$ is equal to $d\ensuremath{-}{d}_{f}$ where $d (=2)$ is the dimension of the system and ${d}_{f}$ is the fractal dimension of a domain wall induced by changes in the boundary conditions. Our value for ${d}_{f}$ 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.