Exact Results for a One-Dimensional Random-Anisotropy Spin Glass
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Spin-glass behaviour induced by random uniaxial anisotropy has recently been discussed by Pelcovits, Pytte and Rudnik /1/. It was found that a random distribution of anisotropy axes destroys the ferromagnetic state and generates a spin-glass state in fewer than four dimensions. This note gives an exact solution for the one-dimensional case. The ground-state spin configuration is represented as a random walk in spin space, which demonstrates clearly the absence of ferromagnetic order. There exists a spectrum of low-lying excitation extending down to zero energy which gives rise to specific properties characteristic of a one-dimensional spin-glass ground state.
KeywordsSpin Space Ferromagnetic Order Configurational Average Magnetic Ground State Full Sphere
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