中国物理B ›› 2002, Vol. 11 ›› Issue (9): 948-954.doi: 10.1088/1009-1963/11/9/318

• CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES • 上一篇    下一篇

Metastability of Ising spin chains with nearest-neighbour and next-nearest-neighbour interactions in random fields

G. Ismail, S. Hassan   

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
  • 收稿日期:2002-03-02 修回日期:2002-05-22 出版日期:2005-06-12 发布日期:2005-06-12

Metastability of Ising spin chains with nearest-neighbour and next-nearest-neighbour interactions in random fields

G. Ismail, S. Hassan   

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
  • Received:2002-03-02 Revised:2002-05-22 Online:2005-06-12 Published:2005-06-12

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摘要： One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.

Abstract: One-dimensional Ising systems in random fields (RFs) are studied taking into account the nearest-neighbour and next-nearest-neighbour interactions. We investigate two distributions of RFs: binary and Gaussian distributions. We consider four cases of the exchange couplings: ferro－ferromagnetic (F－F), ferro－antiferromagnetic (F－AF), antiferro－ferromagnetic (AF－F) and antiferro－antiferromagnetic (AF－AF). The energy minima of chains of no more than 30 spins with periodic boundary conditions are analysed exactly. We found that the average number of energy minima grows exponentially with the number of spins in both cases of RFs. The energy distributions across the corresponding energy minima are shown. The effects of RFs on both the average and density of metastable states are explained. For a weak RF, the energy distributions display a multipartitioned structure. We also discuss the frustration effect due to RFs and exchange fields. Finally, the distributions of magnetization are calculated. The absolute value of magnetization averaged over all metastable states decreases logarithmically with the number of spins.

Key words: random field, metastable states, nearest-neighbour, next-nearest-neighbour, magnetization

中图分类号:  (Classical spin models)

  • 75.10.Hk
75.30.Et (Exchange and superexchange interactions) 75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.)) 75.60.Ej (Magnetization curves, hysteresis, Barkhausen and related effects)