Long-Time Behavior for the 1-D Stochastic Ising Model with Unbounded Random Couplings

被引：0

作者：

H. Spohn

E. Zhizhina

机构：

[1] Technische Universität München,Zentrum Mathematik

[2] Institute for Information Transmission Problems,undefined

来源：

Journal of Statistical Physics | 2003年 / 111卷

关键词：

Spin-flip dynamics; disordered energy; stretched exponential decay;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We consider the ferromagnetic Ising model with Glauber spin flip dynamics in one dimension. The external magnetic field vanishes and the couplings are i.i.d. random variables. If their distribution has compact support, the disorder averaged spin auto-correlation function has an exponential decay in time. We prove that, if the couplings are unbounded, the decay switches to either a power law or a stretched exponential, in general.

引用

页码：419 / 431

页数：12

共 18 条

[1] Minlos R. A.(1994)The complete spectral decomposition of a generator of Glauber dynamics for one-dimensional Ising model Uspechi Mathem. Nauk 49 209-210
[2] Trishch A. G.(1999)Spectral analysis of the disordered stochastic 1-D Ising model Commun. Math. Phys. 204 651-668
[3] Albeverio S.(1994)Strong decay to equilibrium in one-dimensional random spin systems J. Stat. Phys. 77 717-732
[4] Minlos R.(1996)Percolation techniques in disordered spin flip dynamics: relaxation to the unique invariant measure Comm. Math. Phys. 177 83-101
[5] Scacciatelli E.(1995)The uniqueness regime of Gibbs fields with unbounded disorder J. Stat. Phys. 81 829-835
[6] Zhizhina E.(1997)Relaxation of disordered magnets in the Griffiths' regime Comm. Math. Phys. 188 135-173
[7] Zegarlinski B.(1975)Behavior of the density of states in the one-dimensional disordered systems near the spectrum bounds Teoret. Matemat. Physika 23 132-139
[8] Gielis G.(2000)The Lifshitz tail and relaxation to equilibrium in the one-dimensional disordered Ising model J. Stat. Phys. 98 701-721
[9] Maes C.(1963)Time dependent statistics of the Ising model J. Math. Phys. 4 294-307
[10] Gielis G.(undefined)undefined undefined undefined undefined-undefined

← 1 2 →