The distribution of Lee-Yang zeros and Griffiths singularities in the ±j model of spin glasses

Yoshiki Matsuda, Hidetoshi Nishimori, Koji Hukushima

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric ±J Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of a numerical transfer matrix which provides us with the exact expression of the partition function as a polynomial of fugacity. The results show that zeros are distributed in a wide region in the complex field plane. Nevertheless, we observe that zeros on the imaginary axis play dominant roles in the critical behaviour since zeros on the imaginary axis are in closer proximity to the real axis. We estimate the density of zeros on the imaginary axis by an importance-sampling Monte Carlo algorithm, which enables us to sample very rare events. Our result suggests that the density has an essential singularity at the origin. This observation is consistent with the existence of Griffiths singularities in the present systems. This is the first evidence for Griffiths singularities in spin glass systems in equilibrium.

Original languageEnglish
Article number324012
JournalJournal of Physics A: Mathematical and Theoretical
Issue number32
Publication statusPublished - 2008 Aug 15
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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