Droplet model for autocorrelation functions in an Ising ferromagnet

Journal Article · Sat Jul 15 00:00:00 EDT 1989 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.40.995· OSTI ID:6013013

Tang, C; Nakanishi, H; Langer, J S

The autocorrelation function,/ital C/(/ital t/)=/l angle//ital S//sub /ital i//(0)S/sub i/(t)/r angle//minus//l angle/S/sub i//sup 2/ (0)/r angle/, of Ising spins in an ordered phase (/ital T//lt//ital T//sub /ital c//) 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 /ital d/=2, (2) continuous with a finite gap for /ital d/=3, and (3) discrete for /ital d//ge/4. These spectra are different from the gapless form assumed by Takano, Nakanishi, and Miyashita for the kinetic Ising model. The asymptotic form of /ital C/(/ital t/) is found to be exponential for /ital d//ge/3 and stretched exponential with the exponent /beta/=1/2 for /ital d/=2. Our results for /ital C/(/ital t/) are consistent with the scaling argument of Huse and Fisher, but not with Ogielski's Monte Carlo simulations.

• Research Organization: Institute for Theoretical Physics,University of California, Santa Barbara, California 93106 (US)
• OSTI ID: 6013013
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 40:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360104* -- Metals & Alloys-- Physical Properties
CORRELATION FUNCTIONS
CRITICAL TEMPERATURE
CRYSTAL MODELS
FERROMAGNETIC MATERIALS
FLUCTUATIONS
FUNCTIONS
ISING MODEL
MAGNETIC MATERIALS
MATERIALS
MATHEMATICAL MODELS
ORIENTATION
PHYSICAL PROPERTIES
SPIN ORIENTATION
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
VARIATIONS