Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-02-25
Phys. Rev. B 70, 054429 (2004)
Physics
Condensed Matter
Disordered Systems and Neural Networks
10 pages, 10 figures, 3 tables
Scientific paper
10.1103/PhysRevB.70.054429
We analyze exact ground-state energies of two-dimensional Ising spin glasses with either Gaussian or bimodal nearest-neighbor interactions for large system sizes and for three types of boundary conditions: free on both axes, periodic on both axes, and free on one axis and periodic on the other. We find accurate values for bulk-, edge-, and corner-site energies. Fits for the system with Gaussian bonds are excellent for all types of boundary conditions over the whole range of system sizes. In particular, the leading behavior for non-free boundary conditions is governed by the stiffness exponent ~ -0.28 describing the scaling of domain-wall and droplet excitations. For the system with a bimodal distribution of bonds the fit is good for free boundary conditions but worse for other geometries, particularly for periodic-free boundary conditions where there appear to be unorthodox corrections to scaling up to large sizes. Finally, by introducing hard bonds we test explicitly for the Gaussian case the relationship between domain walls and the standard scaling behavior.
Campbell Andrew I.
Hartmann Alexander K.
Katzgraber Helmut G.
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