Relaxation of the spin autocorrelation function in the kinetic Ising model with bond dilution

Hiroshi Takano, Seiji Miyashita

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

The relaxation of the equilibrium correlation function q(t)=N-1 Σi=1N<Si(t)<Si(0)> is studied by the Monte Carlo method for the bond-diluted kinetic Ising model on the square lattice with a bond concentration below the percolation threshold. Here, the system has N Ising spins and Si denotes the i-th Ising spin. The correlation function q(t) seems to exhibit a nonexponential decay below the critical temperature of the nonrandom Ising model. An effective size v of a cluster of ferromagnetically connected spins is defined as v=(In τ)2, where τ is the longest relaxation time in the cluster. It is found that the distribution function of v behaves as P(v) exp [-γv]. Although the asymptotic behavior q(t)∼exp [-C(In t)2] is not reached in the time region studied by the Monte Carlo method, this distribution explains the long-time behavior of q(t).

Original languageEnglish
Pages (from-to)3871-3874
Number of pages4
JournalJournal of the Physical Society of Japan
Volume58
Issue number11
Publication statusPublished - 1989 Nov

Fingerprint

Ising model
autocorrelation
dilution
Monte Carlo method
kinetics
critical temperature
relaxation time
distribution functions
thresholds
decay

Keywords

  • Bond dilution
  • Griffiths singularity
  • Kinetic ising model
  • Relaxation
  • Spin autocorrelation function

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Relaxation of the spin autocorrelation function in the kinetic Ising model with bond dilution. / Takano, Hiroshi; Miyashita, Seiji.

In: Journal of the Physical Society of Japan, Vol. 58, No. 11, 11.1989, p. 3871-3874.

Research output: Contribution to journalArticle

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N2 - The relaxation of the equilibrium correlation function q(t)=N-1 Σi=1N<Si(t)<Si(0)> is studied by the Monte Carlo method for the bond-diluted kinetic Ising model on the square lattice with a bond concentration below the percolation threshold. Here, the system has N Ising spins and Si denotes the i-th Ising spin. The correlation function q(t) seems to exhibit a nonexponential decay below the critical temperature of the nonrandom Ising model. An effective size v of a cluster of ferromagnetically connected spins is defined as v=(In τ)2, where τ is the longest relaxation time in the cluster. It is found that the distribution function of v behaves as P(v) exp [-γv]. Although the asymptotic behavior q(t)∼exp [-C(In t)2] is not reached in the time region studied by the Monte Carlo method, this distribution explains the long-time behavior of q(t).

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