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Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass

Matteo Palassini·A. P. Young
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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-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.

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Matteo Palassini, A. P. Young. 1999-08-19. Trivial Ground State Structure in the Two-Dimensional Ising Spin Glass. https://doi.org/10.1103/physrevb.60.r9919

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