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

Tadashi Kadowaki, Yoshihiko Nonomura, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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 ±J and the site-random models using this method for strips of various sizes up to 5 × ∞. 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 complexfield plane for the Ising ferronmgnet. The ±J Ising model has a series of singularities which may approach a limiting point around p ∼ 0.9 on the real axis in the limit of infinite width.

Original languageEnglish
Pages (from-to)1609-1616
Number of pages8
Journaljournal of the physical society of japan
Issue number6
Publication statusPublished - 1996
Externally publishedYes


  • Ground-state energy
  • Site random ising model
  • Spin glass
  • Transfer matrix
  • ±J ising model

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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