Exact Ground-State Energy of the Ising Spin Glass on Strips

Details Exact Ground-State Energy of the Ising Spin Glass on Strips Exact Ground-State Energy of the Ising Spin Glass on Strips

1996-01-10

arxiv.org/abs/cond-mat/9601033v2

J. Phys. Soc. Jpn. 66 (1996) 1609

Physics

Condensed Matter

10 pages, 12 Postscript figures, LaTeX, uses subeqn.sty, minor changes in tex-file

Scientific paper

10.1143/JPSJ.65.1609

We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for complex values of the probability describing quenched randomness. We study the $\pm J$ and the site-random models using this method for strips of various sizes up to $5\times\infty$. The ground-state energy of these models is found to have singular points in the complex-probability plane, reminiscent of Lee-Yang zeros in the complex-field plane for the Ising ferromagnet. The $\pm J$ Ising model has a series of singularities which may approach a limiting point around $p \sim 0.9$ on the real axis in the limit of infinite width.

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