Lower Critical Dimension of Ising Spin Glasses

Details Lower Critical Dimension of Ising Spin Glasses Lower Critical Dimension of Ising Spin Glasses

2001-07-13

arxiv.org/abs/cond-mat/0107308v1

Phys. Rev. B 64, 180404 (2001)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures, 1 table, revtex

Scientific paper

10.1103/PhysRevB.64.180404

Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be investigated. We study domain walls induced by two rather different types of boundary-condition changes, and, in each case, analyze the system-size dependence of an appropriately defined ``defect energy'', which we denote by DE. For Gaussian disorder, we find a power-law behavior DE ~ L^\theta, with \theta=-0.266(2) and \theta=-0.282(2) for the two types of boundary condition changes. These results are in reasonable agreement with each other, allowing for small systematic effects. They also agree well with earlier work on smaller sizes. The negative value indicates that two dimensions is below the lower critical dimension d_c. For the +-J model, we obtain a different result, namely the domain-wall energy saturates at a nonzero value for L\to \infty, so \theta = 0, indicating that the lower critical dimension for the +-J model exactly d_c=2.

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