Exact results on the single spin-flip Glauber dynamics of six coupled random-field Ising spins with a coordination number of 4 are presented. Two distributions of random fields, a binary distribution (BD) and a Gaussian distribution (GD), are investigated. The effects of the static magnetic field are discussed. In the zero-magnetic-field case, the number of diverging relaxation times is equal to the number of energy minima minus one. This rule is broken in the presence of a magnetic field. The longest relaxation times in the absence of the field verify the Arrhenius law with the 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 GD case, the energy-barrier distribution is continuous while it is quasidiscrete in the BD case.

• Received 23 September 1992

DOI:https://doi.org/10.1103/PhysRevB.47.14237