### Abstract

The autocorrelation function, C(t)= Si(0)Si(t)Si2 (0), of Ising spins in an ordered phase (T<Tc) is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation for droplet fluctuations is studied in detail. The relaxation-rate spectra for the corresponding Fokker-Planck equation are found to be (1) continuous from zero for dimension d=2, (2) continuous with a finite gap for d=3, and (3) discrete for d4. These spectra are different from the gapless form assumed by Takano, Nakanishi, and Miyashita for the kinetic Ising model. The asymptotic form of C(t) is found to be exponential for d3 and stretched exponential with the exponent =1/2 for d=2. Our results for C(t) are consistent with the scaling argument of Huse and Fisher, but not with Ogielskis Monte Carlo simulations.

Original language | English |
---|---|

Pages (from-to) | 995-1003 |

Number of pages | 9 |

Journal | Physical Review A |

Volume | 40 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jan 1 1989 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*40*(2), 995-1003. https://doi.org/10.1103/PhysRevA.40.995

**Droplet model for autocorrelation functions in an Ising ferromagnet.** / Tang, Chao; Nakanishi, Hiizu; Langer, J. S.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 40, no. 2, pp. 995-1003. https://doi.org/10.1103/PhysRevA.40.995

}

TY - JOUR

T1 - Droplet model for autocorrelation functions in an Ising ferromagnet

AU - Tang, Chao

AU - Nakanishi, Hiizu

AU - Langer, J. S.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - The autocorrelation function, C(t)= Si(0)Si(t)Si2 (0), of Ising spins in an ordered phase (T<Tc) is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation for droplet fluctuations is studied in detail. The relaxation-rate spectra for the corresponding Fokker-Planck equation are found to be (1) continuous from zero for dimension d=2, (2) continuous with a finite gap for d=3, and (3) discrete for d4. These spectra are different from the gapless form assumed by Takano, Nakanishi, and Miyashita for the kinetic Ising model. The asymptotic form of C(t) is found to be exponential for d3 and stretched exponential with the exponent =1/2 for d=2. Our results for C(t) are consistent with the scaling argument of Huse and Fisher, but not with Ogielskis Monte Carlo simulations.

AB - The autocorrelation function, C(t)= Si(0)Si(t)Si2 (0), of Ising spins in an ordered phase (T<Tc) is studied via a droplet model. Only noninteracting spherical droplets are considered. The Langevin equation for droplet fluctuations is studied in detail. The relaxation-rate spectra for the corresponding Fokker-Planck equation are found to be (1) continuous from zero for dimension d=2, (2) continuous with a finite gap for d=3, and (3) discrete for d4. These spectra are different from the gapless form assumed by Takano, Nakanishi, and Miyashita for the kinetic Ising model. The asymptotic form of C(t) is found to be exponential for d3 and stretched exponential with the exponent =1/2 for d=2. Our results for C(t) are consistent with the scaling argument of Huse and Fisher, but not with Ogielskis Monte Carlo simulations.

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U2 - 10.1103/PhysRevA.40.995

DO - 10.1103/PhysRevA.40.995

M3 - Article

AN - SCOPUS:0041762301

VL - 40

SP - 995

EP - 1003

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -