Relaxation Modes in Random Spin Systems

Hiroshi Takano, Seiji Miyashita

Research output: Contribution to journalArticlepeer-review

47 Citations (Scopus)


A method of finding slow relaxation modes in random spin systems is proposed. For stochastic dynamics, an approximate relaxation mode {fi} and its relaxation rate λ are determined from an eigenvalue problem ∑j Ci,j(t0 + t)fj = exp (−λt)∑j Ci,j(t0) fj, where Ci,j(t) = 〈Si(t)×Sj(0)〉 is the correlation matrix of spins. The method is applied to the two-dimensional ±J Ising spin glass below the critical temperature of the corresponding nonrandom ferromagnet. It is found through Monte Carlo simulations that the slow relaxation modes obtained by the present method describe the long-time behavior of spins well. The slow relaxation modes are spatially localized and can be regarded as clusters. The distribution of the relaxation rates is consistent with the prediction of the theory which assumes independent motion of clusters.

Original languageEnglish
Pages (from-to)3688-3698
Number of pages11
JournalJournal of the Physical Society of Japan
Issue number10
Publication statusPublished - 1995 Oct


  • Monte Carlo simulations
  • random spin systems
  • relaxation modes
  • spin autocorrelation function
  • the Griffiths singularity
  • the Ising spin glass

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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