The excitations of ferromagnets with liquid-like disorder

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Abstract
The results of two model calculations of the excitations of an amorphous spin-1/2 ferromagnet are presented and compared. The first calculation uses an analytical Green function method in which the disorder-ensemble averaging uses techniques borrowed from the theory of liquids. This analytical theory is expected to produce its best results for dilute systems. The second calculation involves a Monte Carlo simulation of a three-dimensional disordered hard-sphere liquid and uses linearised spin-wave theory to describe the dynamics of the resulting structure. This technique is expected to produce its best results for dense structures. The calculations yield dispersion and density-of-states curves for the spin waves of the system which are in reasonable agreement with each other. The magnetisation and critical temperatures are also obtained. All calculations are performed for several different degrees of disorder.