### Abstract

The relaxation of the equilibrium correlation function q(t)=N^{-1} Σ_{i=1}^{N}<S_{i}(t)<S_{i}(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 S_{i} 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 language | English |
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Pages (from-to) | 3871-3874 |

Number of pages | 4 |

Journal | Journal of the Physical Society of Japan |

Volume | 58 |

Issue number | 11 |

Publication status | Published - 1989 Nov |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*58*(11), 3871-3874.

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

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 58, no. 11, pp. 3871-3874.

}

TY - JOUR

T1 - Relaxation of the spin autocorrelation function in the kinetic Ising model with bond dilution

AU - Takano, Hiroshi

AU - Miyashita, Seiji

PY - 1989/11

Y1 - 1989/11

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).

AB - 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).

KW - Bond dilution

KW - Griffiths singularity

KW - Kinetic ising model

KW - Relaxation

KW - Spin autocorrelation function

UR - http://www.scopus.com/inward/record.url?scp=0342374097&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0342374097&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0342374097

VL - 58

SP - 3871

EP - 3874

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 11

ER -