Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature

1988 ◽  
Vol 37 (7) ◽  
pp. 3716-3719 ◽  
Author(s):  
Hiroshi Takano ◽  
Hiizu Nakanishi ◽  
Seiji Miyashita
Keyword(s):  
Correlation Function ◽  
Critical Temperature ◽  
Ising Model ◽  
Exponential Decay ◽  
Spin Correlation ◽  
Kinetic Ising Model ◽  
Spin Correlation Function ◽  
Stretched Exponential ◽  
Stretched Exponential Decay

MAGNETIZATION DECAY IN THE DILUTED ISING MODEL

1996 ◽  
Vol 07 (01) ◽  
pp. 89-97 ◽  
Author(s):  
PETER GRASSBERGER
Keyword(s):  
Asymptotic Behavior ◽  
Critical Temperature ◽  
Ising Model ◽  
Exponential Decay ◽  
Stretched Exponential ◽  
Damage Spreading ◽  
Monte Carlo Techniques ◽  
Magnetization Decay ◽  
Damage Healing ◽  
Stretched Exponential Decay

Using Monte Carlo techniques, we study the decay of magnetization in diluted two-dimensional Ising models at and below the critical temperature Tc of the undiluted Ising model, but above the critical temperature of the diluted system. Using damage spreading (or rather damage "healing"), we are able to measure down to much lower final magnetizations (10–9) and to much larger times than previous authors. Nevertheless, we do not yet find the predicted asymptotic behavior in the Griffiths phase T < Tc. But we can at least exclude a stretched exponential decay as found in previous papers, for T < Tc. Finally, we discuss the case T = Tc where a stretched exponential decay can be proven to hold, at least for p < pc. We indeed do see a stretched exponential for p = pc (and T = Tc), but we show that it cannot describe the asymptotic behavior either.

OFF THE CRITICAL POINT BY PERTURBATION (II): THE ISING MODEL SPIN-SPIN CORRELATOR IN A MAGNETIC FIELD

1990 ◽  
Vol 04 (05) ◽  
pp. 1039-1047 ◽  
Author(s):  
Vl. S. Dotsenko
Keyword(s):  
Magnetic Field ◽  
Correlation Function ◽  
Ising Model ◽  
Scaling Function ◽  
Spin Correlation ◽  
Regularization Technique ◽  
Spin Correlation Function ◽  
Analytic Regularization ◽  
Spin Correlator ◽  
The Scaling Function

An extension of the analytic regularization technique based on the conform 1 theory is suggested for the case of the spin-spin correlation function of the Ising model in a magnetic field, <σ0σR>h=F(t)/(R)1/4, t=hR15/8. Several first terms of the expansion of the scaling function F(t) are given.

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