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

Abstract

A one-dimensional system of six coupled random field Ising spins is studied by Glauber dynamics. The nearest-neighbour and next-nearest-neighbour interactions are taken into consideration. Two distributions of random fields (RF) – binary and Gaussian distribution – are investigated. We consider four cases of exchange couplings: ferro–ferromagnetic (F–F), ferro–antiferromagnetic (F–AF), antiferro–ferromagnetic (AF–F) and antiferro–antiferromagnetic (AF–AF). The system is fully frustrated, undergoes a zero-temperature phase transition and has multiple local energy minima in both distributions. The dynamics of the four systems are solved exactly in both distributions of RF. The effects of random fields are discussed. The number of diverging relaxation times is equal to the number of energy minima minus one. The longest relaxation times verify the Arrhenius law with energy barrier determined by the energy needed to invert the ground-state spin configuration. At low temperatures, according to the Arrhenius law, the spectrum of relaxation times shows a double-peak distribution on a logarithmic scale. In the Gaussian distribution of RF the energy-barrier distribution is continuous while it is quasi-discrete in the binary distribution. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)