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

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

1999-04-14

arxiv.org/abs/cond-mat/9904206v2

Phys.Rev. B60 (1999) 9919

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 3 postscript figures; some changes in response to referees' comments, to appear in Phys Rev. B, Rapid Communications,

Scientific paper

10.1103/PhysRevB.60.R9919

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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