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#### Exact ground states of two-dimensional $\pm J$ Ising Spin Glasses

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##### Fulltext (public)

1996-1-004

(Any fulltext), 11KB

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##### Citation

De Simone, C., Diehl, M., Jünger, M., Mutzel, P., Reinelt, G., & Rinaldi, G.(1996).
*Exact ground states of two-dimensional $\pm J$ Ising Spin Glasses* (MPI-I-1996-1-004). Saarbrücken:
Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A1A4-F

##### Abstract

In this paper we study the problem of finding an exact ground state of a two-dimensional $\pm J$ Ising spin glass on a square lattice with nearest neighbor interactions and periodic boundary conditions when there is
a concentration $p$ of negative bonds, with $p$ ranging between $0.1$ and $0.9$. With our exact algorithm we can determine ground states of grids of sizes up to $50\times 50$ in a moderate amount of computation time (up to one hour each) for several values of $p$. For the ground state energy of an infinite spin glass system with $p=0.5$ we estimate $E_{0.5}^\infty = -1.4015 \pm0.0008$.
We report on extensive computational tests based on more than $22\,000$ experiments.